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Geometry -- Textbooks

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Broader terms:Narrower terms:Filed under: Geometry -- Textbooks
  • [Info]CK-12 Geometry (c2011), by Victor Cifarelli, Andrew Gloag, Dan Greenberg, Jim Sconyers, and Bill Zahner (multiple formats at
Filed under: Topology -- TextbooksFiled under: Trigonometry -- Textbooks
  • [Info]CK-12 Trigonometry (second edition, c2011), by Art Fortgang, Andrea Hayes, Lori Jordan, Mara Landers, Brenda Meery, and Larry Ottman (multiple formats at
  • [Info]Trigonometry (electronic edition, 2013 or later), by Michael Corral (PDF with commentary at

Items below (if any) are from related and broader terms.

Filed under: Geometry
  • [Info]Geometry Unbound (c2006), by Kiran Sridhara Kedlaya (PDF with commentary at kskedlayaorg)
  • [Info]Geometric Topology: Localization, Periodicity and Galois Symmetry (The 1970 MIT Notes) (electronic edition, ca. 2005), by Dennis Sullivan, ed. by Andrew Ranicki (PDF in the UK)
  • [Info]Model Theory, Algebra, and Geometry (2000), ed. by Deirdre Haskell, Anand Pillay, and Charles Steinhorn (PDF files with commentary at
  • [Info]Cours de Géométrie Élémentaire, avec de Nombreux Exercices (second edition, in French; Tours: A. Mame et fils; et al., 1912), by G. Marie (page images at HathiTrust; US access only)
  • [Info]An Elementary Treatise on Modern Pure Geometry, by R. Lachlan (page images at Cornell)
  • [Info]Elements of Geometry and Trigonometry, by A. M. Legendre and Charles Davies, ed. by J. Howard Van Amringe (page images at Cornell)
  • [Info]The First Six Books of the Elements of Euclid, and Propositions I.-XXI. of Book XI., and an Appendix on the Cylinder, Sphere, Cone, Etc., With Copious Annotations and Numerous Exercises (Dublin: Hodges, Figgis and Co., 1885), by Euclid and John Casey (page images at Cornell)
  • [Info]Geometriske Eksperimenter (in Danish; Copenhagen: Jul. Gjellerups Forlag, 1913), by Johannes Hjelmslev (multiple formats at
  • [Info]An Elementary Treatise on Pure Geometry with Numerous Examples, by John Wellesley Russell (page images at Cornell)
  • [Info]La Recente Geometria del Triangolo (in Italian; Città di Castello: S. Lapi, 1900), by Cristoforo Alasia
  • [Info]Lectures on Fundamental Concepts of Algebra and Geometry (1911), by John Wesley Young (page images at Cornell)
Filed under: Geometry -- Computer simulationFiled under: Geometry -- Computer-assisted instructionFiled under: Geometry -- CongressesFiled under: Geometry -- Data processingFiled under: Geometry -- Early works to 1800
  • [Info]Euclid's Elements of Geometry (Greek text from Heiberg's edition, with English translation and notes by the editor; 2008), by Euclid, ed. by Richard Fitzpatrick, contrib. by J. L. Heiberg (PDF with commentary at Texas)
  • [Info]Brouillon Project d'une Atteinte aux Evenemens des Rencontres du Cone avec un Plan, par L,S,G,D,L (in French; 1639), by Gérard Desargues
  • [Info]Francisci à Schooten Principia Matheseos Universalis, seu Introductio ad Geometriae Methodum Renati Des Cartes (in Latin; Leiden: Ex Officinâ Elseviriorum, 1651), by Frans van Schooten, ed. by Erasmus Bartholin
  • [Info]Aritmetica, e Geometria Prattica (in Italian; Naples: C. Troyse and G.-D. Pietroboni, 1697), by Elia del Re
  • [Info]Aritmetica, e Geometria Prattica (in Italian; Naples: N. Migliaccio, 1733), by Elia del Re (multiple formats at Google)
  • [Info]Pyrotechnia: or, A Discourse of Artificial Fire-Works... Whereunto is Annexed a Short Treatise of Geometrie (1635), by John Babington (frame- and cookie-dependent page images here at Penn)
  • [Info]Utriusque Cosmi Maioris Scilicet et Minoris Metaphysica, Physica atque Technica Historia (2 volumes, in Latin; ca. 1617), by Robert Fludd
  • [Info]Euclidis Elementa (5 volumes in Greek and Latin; Leipzig: B. G. Teubner, 1883-1888), by Euclid, ed. by J. L. Heiberg
  • [Info]The Geometrical Lectures of Isaac Barrow, by Isaac Barrow, trans. by J. M. Child (page images at Cornell)
  • [Info]Geometrical Solutions Derived From Mechanics: A Treatise of Archimedes (with LaTeX markup), by Archimedes, trans. by J. L. Heiberg and Lydia Gillingham Robinson, contrib. by David Eugene Smith (Gutenberg text)
  • [Info]The Geometry of René Descartes, by René Descartes, trans. by David Eugene Smith and Marcia L. Latham (PDF at
  • [Info]Tychonis Brahe Triangulorum Planorum et Sphaericorum Praxis Arithmetica, Qua Maximus Eorum Praesertim in Astronomicis Usus Compendiose Explicatur (facsimile of a 1591 manuscript attributed by Studnicka to Brahe, with notes, in Latin; Prague: Ex Officina Polygraphica Ios. Farsky, 1886), by Tycho Brahe, ed. by F. I. Studnicka (page images at HathiTrust)
  • [Info]Elements, by Euclid, ed. by D. E. Joyce, trans. by Thomas Little Heath (illustrated HTML at
  • [Info]Elements (English and Greek), by Euclid, trans. by Thomas Little Heath (HTML with commentary at Perseus)
  • [Info]Harmonies of the World, by Johannes Kepler, trans. by Charles Glenn Wallis (HTML with commentary at
  • [Info]The Method of Archimedes, Recently Discovered by Heiberg: A Supplement to the Works of Archimedes, 1897 (Cambridge: At the University Press, 1912), by Archimedes, ed. by Thomas Little Heath, contrib. by J. L. Heiberg (multiple formats at
  • [Info]The Works of Archimedes, Edited in Modern Notation With Introductory Chapters (Cambridge: At the University Press, 1897), by Archimedes, ed. by Thomas Little Heath (multiple formats at
Filed under: Geometry -- FoundationsFiled under: Geometry -- HistoryFiled under: Geometry -- MiscellaneaFiled under: Geometry -- PeriodicalsFiled under: Geometry -- PhilosophyFiled under: Geometry -- Problems, exercises, etc.
  • [Info]Paper Folding for the Mathematics Class (Washington: National Council of Teachers of Mathematics, c1957), by Donovan A. Johnson (page images at HathiTrust)
  • [Info]Advanced Problems in Mathematics: Preparing for University (Cambridge, UK: Open Book Publishers, 2016), by S. T. C. Siklos (multiple formats with commentary at Open Book Publishers)
  • [Info]Méthodes et Théories pour la Resolution des Problèmes de Constructions Géométriques, Avec Application à Plus de 400 Problèmes (third edition, in French; Paris: Gauthier-Villars et fils; Copenhagen: A. F. Høst et fils, 1901), by Julius Petersen, trans. by Octave Chemin (multiple formats at
  • [Info]Methods and Theories for the Solution of Problems of Geometrical Constructions, Applied to 410 Problems (Copenhagen: A. F. Høst and Son; London: S. Low, Marston, Searle and Rivington, 1879), by Julius Petersen, trans. by Sophus Haagensen
  • [Info]A Key to the Exercises in the First Six Books of Casey's Elements of Euclid, by Joseph Casey (page images at Cornell)

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Boost kids" confidence and target the key math skills they need to succeed on standardized tests with this collection of 40 super-fun math puzzles. These puzzles provide the engaging, hands-on practice students need to master geometry and measurement. Also includes reproducible student tip pages with helpful strategies. Perfect to use for level-appropriate, easy-to-manage homework, and for getting kids excited about math.

Boost kids" confidence and target the key math skills they need to succeed on standardized tests with this collection of 40 super-fun math puzzles. These puzzles provide the engaging, hands-on practice students need to master geometry and measurement. Also includes reproducible student tip pages with helpful strategies. Perfect to use for level-appropriate, easy-to-manage homework, and for getting kids excited about math.

Teacher Tips

You may find it helpful to assign certain puzzles as practice word to follow a lesson, as review work, or as homework. You also may want to have students work on different puzzles depending on the skills each student needs to practice. Almost every activity is self-correcting—whether they are solving a riddle or breaking a code, students are encouraged to check each problem so they can finish the puzzle successfully!

You may find it helpful to assign certain puzzles as practice word to follow a lesson, as review work, or as homework. You also may want to have students work on different puzzles depending on the skills each student needs to practice. Almost every activity is self-correcting—whether they are solving a riddle or breaking a code, students are encouraged to check each problem so they can finish the puzzle successfully!

Product Details

  • Item #:NTS541019
  • ISBN13:9780545410199
  • Format:eBook
  • File Format:pdf
  • Grades:4 - 6

Fun Independent Practice Pages: Geometry and Measurement



5th std Mathematics-Term 1 Unit-1 Geometry-Symmetry \u0026 Nets of 3D shapes-pages 11-16

Euclid's Elements

Mathematical treatise by Euclid

The Elements (Ancient Greek: ΣτοιχεῖονStoikheîon) is a mathematicaltreatise consisting of 13 books attributed to the ancient Greek mathematicianEuclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.

Euclid's Elements has been referred to as the most successful[a][b] and influential[c]textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing in 1482, the number reaching well over one thousand.[d] For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.

Geometry emerged as an indispensable part of the standard education of the English gentleman in the eighteenth century; by the Victorian period it was also becoming an important part of the education of artisans, children at Board Schools, colonial subjects and, to a rather lesser degree, women. The standard textbook for this purpose was none other than Euclid's The Elements.


Basis in earlier work[edit]

An illumination from a manuscript based on Adelard of Bath's translation of the Elements, c. 1309–1316; Adelard's is the oldest surviving translation of the Elementsinto Latin, done in the 12th-century work and translated from Arabic.

Scholars believe that the Elements is largely a compilation of propositions based on books by earlier Greek mathematicians.

Proclus (412–485 AD), a Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the Elements: "Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors".

Pythagoras (c. 570–495 BC) was probably the source for most of books I and II, Hippocrates of Chios (c. 470–410 BC, not the better known Hippocrates of Kos) for book III, and Eudoxus of Cnidus (c. 408–355 BC) for book V, while books IV, VI, XI, and XII probably came from other Pythagorean or Athenian mathematicians. The Elements may have been based on an earlier textbook by Hippocrates of Chios, who also may have originated the use of letters to refer to figures.

Transmission of the text[edit]

In the fourth century AD, Theon of Alexandria produced an edition of Euclid which was so widely used that it became the only surviving source until François Peyrard's 1808 discovery at the Vatican of a manuscript not derived from Theon's. This manuscript, the Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions.[7]Papyrus Oxyrhynchus 29 is a tiny fragment of an even older manuscript, but only contains the statement of one proposition.

Although known to Cicero, for instance, no record exists of the text having been translated into Latin prior to Boethius in the fifth or sixth century. The Arabs received the Elements from the Byzantines around 760; this version was translated into Arabic under Harun al Rashid c. 800. The Byzantine scholar Arethas commissioned the copying of one of the extant Greek manuscripts of Euclid in the late ninth century. Although known in Byzantium, the Elements was lost to Western Europe until about 1120, when the English monk Adelard of Bath translated it into Latin from an Arabic translation.[e]

Euclidis – Elementorum libri XV Paris, Hieronymum de Marnef & Guillaume Cavelat, 1573 (second edition after the 1557 ed.); in 8:350, (2)pp. THOMAS–STANFORD, Early Editions of Euclid's Elements, n°32. Mentioned in T.L. Heath's translation. Private collection Hector Zenil.

The first printed edition appeared in 1482 (based on Campanus of Novara's 1260 edition), and since then it has been translated into many languages and published in about a thousand different editions. Theon's Greek edition was recovered in 1533. In 1570, John Dee provided a widely respected "Mathematical Preface", along with copious notes and supplementary material, to the first English edition by Henry Billingsley.

Copies of the Greek text still exist, some of which can be found in the Vatican Library and the Bodleian Library in Oxford. The manuscripts available are of variable quality, and invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text (copies of which are no longer available).

Ancient texts which refer to the Elements itself, and to other mathematical theories that were current at the time it was written, are also important in this process. Such analyses are conducted by J. L. Heiberg and Sir Thomas Little Heath in their editions of the text.

Also of importance are the scholia, or annotations to the text. These additions, which often distinguished themselves from the main text (depending on the manuscript), gradually accumulated over time as opinions varied upon what was worthy of explanation or further study.


A page with marginalia from the first printed edition of Elements, printed by Erhard Ratdoltin 1482

The Elements is still considered a masterpiece in the application of logic to mathematics. In historical context, it has proven enormously influential in many areas of science. Scientists Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, Albert Einstein and Sir Isaac Newton were all influenced by the Elements, and applied their knowledge of it to their work.[11][12] Mathematicians and philosophers, such as Thomas Hobbes, Baruch Spinoza, Alfred North Whitehead, and Bertrand Russell, have attempted to create their own foundational "Elements" for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced.

The austere beauty of Euclidean geometry has been seen by many in western culture as a glimpse of an otherworldly system of perfection and certainty. Abraham Lincoln kept a copy of Euclid in his saddlebag, and studied it late at night by lamplight; he related that he said to himself, "You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight".[14]Edna St. Vincent Millay wrote in her sonnet "Euclid alone has looked on Beauty bare", "O blinding hour, O holy, terrible day, When first the shaft into his vision shone Of light anatomized!". Albert Einstein recalled a copy of the Elements and a magnetic compass as two gifts that had a great influence on him as a boy, referring to the Euclid as the "holy little geometry book".[15][16]

The success of the Elements is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid. Much of the material is not original to him, although many of the proofs are his. However, Euclid's systematic development of his subject, from a small set of axioms to deep results, and the consistency of his approach throughout the Elements, encouraged its use as a textbook for about 2,000 years. The Elements still influences modern geometry books. Furthermore, its logical, axiomatic approach and rigorous proofs remain the cornerstone of mathematics.

In modern mathematics[edit]

One of the most notable influences of Euclid on modern mathematics is the discussion of the parallel postulate. In Book I, Euclid lists five postulates, the fifth of which stipulates

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

The different versions of the parallel postulate result in different geometries.

This postulate plagued mathematicians for centuries due to its apparent complexity compared with the other four postulates. Many attempts were made to prove the fifth postulate based on the other four, but they never succeeded. Eventually in 1829, mathematician Nikolai Lobachevsky published a description of acute geometry (or hyperbolic geometry), a geometry which assumed a different form of the parallel postulate. It is in fact possible to create a valid geometry without the fifth postulate entirely, or with different versions of the fifth postulate (elliptic geometry). If one takes the fifth postulate as a given, the result is Euclidean geometry.


  • Book 1 contains 5 postulates (including the famous parallel postulate) and 5 common notions, and covers important topics of plane geometry such as the Pythagorean theorem, equality of angles and areas, parallelism, the sum of the angles in a triangle, and the construction of various geometric figures.
  • Book 2 contains a number of lemmas concerning the equality of rectangles and squares, sometimes referred to as "geometric algebra", and concludes with a construction of the golden ratio and a way of constructing a square equal in area to any rectilineal plane figure.
  • Book 3 deals with circles and their properties: finding the center, inscribed angles, tangents, the power of a point, Thales' theorem.
  • Book 4 constructs the incircle and circumcircle of a triangle, as well as regular polygons with 4, 5, 6, and 15 sides.
  • Book 5, on proportions of magnitudes, gives the highly sophisticated theory of proportion probably developed by Eudoxus, and proves properties such as "alternation" (if a : b :: c : d, then a : c :: b : d).
  • Book 6 applies proportions to plane geometry, especially the construction and recognition of similar figures.
  • Book 7 deals with elementary number theory: divisibility, prime numbers and their relation to composite numbers, Euclid's algorithm for finding the greatest common divisor, finding the least common multiple.
  • Book 8 deals with the construction and existence of geometric sequences of integers.
  • Book 9 applies the results of the preceding two books and gives the infinitude of prime numbers and the construction of all even perfect numbers.
  • Book 10 proves the irrationality of the square roots of non-square integers (e.g. {\sqrt {2}}) and classifies the square roots of incommensurable lines into thirteen disjoint categories. Euclid here introduces the term "irrational", which has a different meaning than the modern concept of irrational numbers. He also gives a formula to produce Pythagorean triples.[17]
  • Book 11 generalizes the results of book 6 to solid figures: perpendicularity, parallelism, volumes and similarity of parallelepipeds.
  • Book 12 studies the volumes of cones, pyramids, and cylinders in detail by using the method of exhaustion, a precursor to integration, and shows, for example, that the volume of a cone is a third of the volume of the corresponding cylinder. It concludes by showing that the volume of a sphere is proportional to the cube of its radius (in modern language) by approximating its volume by a union of many pyramids.
  • Book 13 constructs the five regular Platonic solids inscribed in a sphere and compares the ratios of their edges to the radius of the sphere.
Definitions 23211718422--1628--131
Postulates 5------------5
Common Notions 5------------5
Propositions 481437162533392736115391818465

Euclid's method and style of presentation[edit]

• "To draw a straight line from any point to any point."
• "To describe a circle with any center and distance."

Euclid, Elements, Book I, Postulates 1 & 3.

An animation showing how Euclid constructed a hexagon (Book IV, Proposition 15). Every two-dimensional figure in the Elementscan be constructed using only a compass and straightedge.

Euclid's axiomatic approach and constructive methods were widely influential.

Many of Euclid's propositions were constructive, demonstrating the existence of some figure by detailing the steps he used to construct the object using a compass and straightedge. His constructive approach appears even in his geometry's postulates, as the first and third postulates stating the existence of a line and circle are constructive. Instead of stating that lines and circles exist per his prior definitions, he states that it is possible to 'construct' a line and circle. It also appears that, for him to use a figure in one of his proofs, he needs to construct it in an earlier proposition. For example, he proves the Pythagorean theorem by first inscribing a square on the sides of a right triangle, but only after constructing a square on a given line one proposition earlier.

As was common in ancient mathematical texts, when a proposition needed proof in several different cases, Euclid often proved only one of them (often the most difficult), leaving the others to the reader. Later editors such as Theon often interpolated their own proofs of these cases.

Propositions plotted with lines connected from Axiomson the top and other preceding propositions, labelled by book.

Euclid's presentation was limited by the mathematical ideas and notations in common currency in his era, and this causes the treatment to seem awkward to the modern reader in some places. For example, there was no notion of an angle greater than two right angles, the number 1 was sometimes treated separately from other positive integers, and as multiplication was treated geometrically he did not use the product of more than 3 different numbers. The geometrical treatment of number theory may have been because the alternative would have been the extremely awkward Alexandrian system of numerals.

The presentation of each result is given in a stylized form, which, although not invented by Euclid, is recognized as typically classical. It has six different parts: First is the 'enunciation', which states the result in general terms (i.e., the statement of the proposition). Then comes the 'setting-out', which gives the figure and denotes particular geometrical objects by letters. Next comes the 'definition' or 'specification', which restates the enunciation in terms of the particular figure. Then the 'construction' or 'machinery' follows. Here, the original figure is extended to forward the proof. Then, the 'proof' itself follows. Finally, the 'conclusion' connects the proof to the enunciation by stating the specific conclusions drawn in the proof, in the general terms of the enunciation.

No indication is given of the method of reasoning that led to the result, although the Data does provide instruction about how to approach the types of problems encountered in the first four books of the Elements. Some scholars have tried to find fault in Euclid's use of figures in his proofs, accusing him of writing proofs that depended on the specific figures drawn rather than the general underlying logic, especially concerning Proposition II of Book I. However, Euclid's original proof of this proposition, is general, valid, and does not depend on the figure used as an example to illustrate one given configuration.


Euclid's list of axioms in the Elements was not exhaustive, but represented the principles that were the most important. His proofs often invoke axiomatic notions which were not originally presented in his list of axioms. Later editors have interpolated Euclid's implicit axiomatic assumptions in the list of formal axioms.

For example, in the first construction of Book 1, Euclid used a premise that was neither postulated nor proved: that two circles with centers at the distance of their radius will intersect in two points. Later, in the fourth construction, he used superposition (moving the triangles on top of each other) to prove that if two sides and their angles are equal, then they are congruent; during these considerations he uses some properties of superposition, but these properties are not described explicitly in the treatise. If superposition is to be considered a valid method of geometric proof, all of geometry would be full of such proofs. For example, propositions I.1 – I.3 can be proved trivially by using superposition.

Mathematician and historian W. W. Rouse Ball put the criticisms in perspective, remarking that "the fact that for two thousand years [the Elements] was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose."


It was not uncommon in ancient times to attribute to celebrated authors works that were not written by them. It is by these means that the apocryphal books XIV and XV of the Elements were sometimes included in the collection. The spurious Book XIV was probably written by Hypsicles on the basis of a treatise by Apollonius. The book continues Euclid's comparison of regular solids inscribed in spheres, with the chief result being that the ratio of the surfaces of the dodecahedron and icosahedron inscribed in the same sphere is the same as the ratio of their volumes, the ratio being

{\displaystyle {\sqrt {\frac {10}{3(5-{\sqrt {5}})}}}={\sqrt {\frac {5+{\sqrt {5}}}{6}}}.}

The spurious Book XV was probably written, at least in part, by Isidore of Miletus. This book covers topics such as counting the number of edges and solid angles in the regular solids, and finding the measure of dihedral angles of faces that meet at an edge.[f]


  • 1460s, Regiomontanus (incomplete)
  • 1482, Erhard Ratdolt (Venice), first printed edition[28]
  • 1533, editio princeps by Simon Grynäus
  • 1557, by Jean Magnien and Pierre de Montdoré [fr], reviewed by Stephanus Gracilis (only propositions, no full proofs, includes original Greek and the Latin translation)
  • 1572, Commandinus Latin edition
  • 1574, Christoph Clavius


  • 1505, Bartolomeo Zamberti [de] (Latin)
  • 1543, Niccolò Tartaglia (Italian)
  • 1557, Jean Magnien and Pierre de Montdoré, reviewed by Stephanus Gracilis (Greek to Latin)
  • 1558, Johann Scheubel (German)
  • 1562, Jacob Kündig (German)
  • 1562, Wilhelm Holtzmann (German)
  • 1564–1566, Pierre Forcadel [fr] de Béziers (French)
  • 1570, Henry Billingsley (English)
  • 1572, Commandinus (Latin)
  • 1575, Commandinus (Italian)
  • 1576, Rodrigo de Zamorano (Spanish)
  • 1594, Typographia Medicea (edition of the Arabic translation of The Recension of Euclid's "Elements"
  • 1604, Jean Errard [fr] de Bar-le-Duc (French)
  • 1606, Jan Pieterszoon Dou (Dutch)
  • 1607, Matteo Ricci, Xu Guangqi (Chinese)
  • 1613, Pietro Cataldi (Italian)
  • 1615, Denis Henrion (French)
  • 1617, Frans van Schooten (Dutch)
  • 1637, L. Carduchi (Spanish)
  • 1639, Pierre Hérigone (French)
  • 1651, Heinrich Hoffmann (German)
  • 1651, Thomas Rudd (English)
  • 1660, Isaac Barrow (English)
  • 1661, John Leeke and Geo. Serle (English)
  • 1663, Domenico Magni (Italian from Latin)
  • 1672, Claude François Milliet Dechales (French)
  • 1680, Vitale Giordano (Italian)
  • 1685, William Halifax (English)
  • 1689, Jacob Knesa (Spanish)
  • 1690, Vincenzo Viviani (Italian)
  • 1694, Ant. Ernst Burkh v. Pirckenstein (German)
  • 1695, Claes Jansz Vooght (Dutch)
  • 1697, Samuel Reyher (German)
  • 1702, Hendrik Coets (Dutch)
  • 1705, Charles Scarborough (English)
  • 1708, John Keill (English)
  • 1714, Chr. Schessler (German)
  • 1714, W. Whiston (English)
  • 1720s, Jagannatha Samrat (Sanskrit, based on the Arabic translation of Nasir al-Din al-Tusi)
  • 1731, Guido Grandi (abbreviation to Italian)
  • 1738, Ivan Satarov (Russian from French)
  • 1744, Mårten Strömer (Swedish)
  • 1749, Dechales (Italian)
  • 1745, Ernest Gottlieb Ziegenbalg (Danish)
  • 1752, Leonardo Ximenes (Italian)
  • 1756, Robert Simson (English)
  • 1763, Pibo Steenstra (Dutch)
  • 1768, Angelo Brunelli (Portuguese)
  • 1773, 1781, J. F. Lorenz (German)
  • 1780, Baruch Schick of Shklov (Hebrew)[31]
  • 1781, 1788 James Williamson (English)
  • 1781, William Austin (English)
  • 1789, Pr. Suvoroff nad Yos. Nikitin (Russian from Greek)
  • 1795, John Playfair (English)
  • 1803, H.C. Linderup (Danish)
  • 1804, François Peyrard (French). Peyrard discovered in 1808 the Vaticanus Graecus 190, which enables him to provide a first definitive version in 1814–1818
  • 1807, Józef Czech (Polish based on Greek, Latin and English editions)
  • 1807, J. K. F. Hauff (German)
  • 1818, Vincenzo Flauti (Italian)
  • 1820, Benjamin of Lesbos (Modern Greek)
  • 1826, George Phillips (English)
  • 1828, Joh. Josh and Ign. Hoffmann (German)
  • 1828, Dionysius Lardner (English)
  • 1833, E. S. Unger (German)
  • 1833, Thomas Perronet Thompson (English)
  • 1836, H. Falk (Swedish)
  • 1844, 1845, 1859, P. R. Bråkenhjelm (Swedish)
  • 1850, F. A. A. Lundgren (Swedish)
  • 1850, H. A. Witt and M. E. Areskong (Swedish)
  • 1862, Isaac Todhunter (English)
  • 1865, Sámuel Brassai (Hungarian)
  • 1873, Masakuni Yamada (Japanese)
  • 1880, Vachtchenko-Zakhartchenko (Russian)
  • 1897, Thyra Eibe (Danish)
  • 1901, Max Simon (German)
  • 1907, František Servít (Czech)
  • 1908, Thomas Little Heath (English)
  • 1939, R. Catesby Taliaferro (English)
  • 1999, Maja Hudoletnjak Grgić (Book I-VI) (Croatian)
  • 2009, Irineu Bicudo (Brazilian Portuguese)
  • 2019, Ali Sinan Sertöz (Turkish)

Currently in print[edit]

  • Euclid's Elements – All thirteen books complete in one volume, Based on Heath's translation, Green Lion Press ISBN 1-888009-18-7.
  • The Elements: Books I–XIII – Complete and Unabridged, (2006) Translated by Sir Thomas Heath, Barnes & Noble ISBN 0-7607-6312-7.
  • The Thirteen Books of Euclid's Elements, translation and commentaries by Heath, Thomas L. (1956) in three volumes. Dover Publications. ISBN 0-486-60088-2 (vol. 1), ISBN 0-486-60089-0 (vol. 2), ISBN 0-486-60090-4 (vol. 3)

Free versions[edit]

  • Euclid's Elements Redux, Volume 1, contains books I–III, based on John Casey's translation.
  • Euclid's Elements Redux, Volume 2, contains books IV–VIII, based on John Casey's translation.



  1. ^Wilson 2006, p. 278 states, "Euclid's Elements subsequently became the basis of all mathematical education, not only in the Roman and Byzantine periods, but right down to the mid-20th century, and it could be argued that it is the most successful textbook ever written."
  2. ^Boyer 1991, p. 100 notes, "As teachers at the school he called a band of leading scholars, among whom was the author of the most fabulously successful mathematics textbook ever written – the Elements (Stoichia) of Euclid".
  3. ^Boyer 1991, p. 119 notes, "The Elements of Euclid not only was the earliest major Greek mathematical work to come down to us, but also the most influential textbook of all times. [...]The first printed versions of the Elements appeared at Venice in 1482, one of the very earliest of mathematical books to be set in type; it has been estimated that since then at least a thousand editions have been published. Perhaps no book other than the Bible can boast so many editions, and certainly no mathematical work has had an influence comparable with that of Euclid's Elements".
  4. ^Bunt, Jones & Bedient 1988, p. 142 state, "the Elements became known to Western Europe via the Arabs and the Moors. There, the Elements became the foundation of mathematical education. More than 1000 editions of the Elements are known. In all probability, it is, next to the Bible, the most widely spread book in the civilization of the Western world."
  5. ^One older work claims Adelard disguised himself as a Muslim student to obtain a copy in Muslim Córdoba. However, more recent biographical work has turned up no clear documentation that Adelard ever went to Muslim-ruled Spain, although he spent time in Norman-ruled Sicily and Crusader-ruled Antioch, both of which had Arabic-speaking populations. Charles Burnett, Adelard of Bath: Conversations with his Nephew (Cambridge, 1999); Charles Burnett, Adelard of Bath (University of London, 1987).
  6. ^Boyer 1991, pp. 118–119 writes, "In ancient times it was not uncommon to attribute to a celebrated author works that were not by him; thus, some versions of Euclid's Elements include a fourteenth and even a fifteenth book, both shown by later scholars to be apocryphal. The so-called Book XIV continues Euclid's comparison of the regular solids inscribed in a sphere, the chief results being that the ratio of the surfaces of the dodecahedron and icosahedron inscribed in the same sphere is the same as the ratio of their volumes, the ratio being that of the edge of the cube to the edge of the icosahedron, that is, {\sqrt {10/[3(5-{\sqrt {5}})]}}. It is thought that this book may have been composed by Hypsicles on the basis of a treatise (now lost) by Apollonius comparing the dodecahedron and icosahedron. [...] The spurious Book XV, which is inferior, is thought to have been (at least in part) the work of Isidore of Miletus (fl. ca. A.D. 532), architect of the cathedral of Holy Wisdom (Hagia Sophia) at Constantinople. This book also deals with the regular solids, counting the number of edges and solid angles in the solids, and finding the measures of the dihedral angles of faces meeting at an edge.


  1. ^The Earliest Surviving Manuscript Closest to Euclid's Original Text (Circa 850); an imageArchived 2009-12-20 at the Wayback Machine of one page
  2. ^Andrew., Liptak (2 September 2017). "One of the world's most influential math texts is getting a beautiful, minimalist edition". The Verge.
  3. ^Grabiner., Judith. "How Euclid once ruled the world". Plus Magazine.
  4. ^Euclid as Founding Father
  5. ^Herschbach, Dudley. "Einstein as a Student"(PDF). Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA. p. 3. Archived from the original(PDF) on 2009-02-26.: about Max Talmud visited on Thursdays for six years.
  6. ^Prindle, Joseph. "Albert Einstein - Young Einstein". Archived from the original on 10 June 2017. Retrieved 29 April 2018.
  7. ^Joyce, D. E. (June 1997), "Book X, Proposition XXIX", Euclid's Elements, Clark University
  8. ^Alexanderson & Greenwalt 2012, p. 163
  9. ^"JNUL Digitized Book Repository". 22 June 2009. Archived from the original on 22 June 2009. Retrieved 29 April 2018.


  • Alexanderson, Gerald L.; Greenwalt, William S. (2012), "About the cover: Billingsley's Euclid in English", Bulletin of the American Mathematical Society, New Series, 49 (1): 163–167, doi:10.1090/S0273-0979-2011-01365-9
  • Artmann, Benno: Euclid – The Creation of Mathematics. New York, Berlin, Heidelberg: Springer 1999, ISBN 0-387-98423-2
  • Ball, Walter William Rouse (1908). A Short Account of the History of Mathematics (4th ed.). Dover Publications.
  • Boyer, Carl B. (1991). "Euclid of Alexandria". A History of Mathematics (Second ed.). John Wiley & Sons. ISBN .
  • Bunt, Lucas Nicolaas Hendrik; Jones, Phillip S.; Bedient, Jack D. (1988). The Historical Roots of Elementary Mathematics. Dover.
  • Busard, H.L.L. (2005). "Introduction to the Text". Campanus of Novara and Euclid's Elements. Stuttgart: Franz Steiner Verlag. ISBN .
  • Callahan, Daniel; Casey, John (2015). Euclid's "Elements" Redux.
  • Dodgson, Charles L.; Hagar, Amit (2009). "Introduction". Euclid and His Modern Rivals. Cambridge University Press. ISBN .
  • Hartshorne, Robin (2000). Geometry: Euclid and Beyond (2nd ed.). New York, NY: Springer. ISBN .
  • Heath, Thomas L. (1956a). The Thirteen Books of Euclid's Elements. 1. Books I and II (2nd ed.). New York: Dover Publications. OL 22193354M.
  • Heath, Thomas L. (1956b). The Thirteen Books of Euclid's Elements. 2. Books III to IX (2nd ed.). New York: Dover Publications. OL 7650092M.
  • Heath, Thomas L. (1956c). The Thirteen Books of Euclid's Elements. 3. Books X to XIII and Appendix (2nd ed.). New York: Dover Publications. OCLC 929205858. Heath's authoritative translation plus extensive historical research and detailed commentary throughout the text.
  • Heath, Thomas L. (1963). A Manual of Greek Mathematics. Dover Publications. ISBN .
  • Ketcham, Henry (1901). The Life of Abraham Lincoln. New York: Perkins Book Company.
  • Nasir al-Din al-Tusi (1594). Kitāb taḥrīr uṣūl li-Uqlīdus [The Recension of Euclid's "Elements"] (in Arabic).
  • Reynolds, Leighton Durham; Wilson, Nigel Guy (9 May 1991). Scribes and scholars: a guide to the transmission of Greek and Latin literature (2nd ed.). Oxford: Clarendon Press. ISBN .
  • Russell, Bertrand (2013). History of Western Philosophy: Collectors Edition. Routledge. ISBN .
  • Sarma, K.V. (1997). Selin, Helaine (ed.). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. ISBN .
  • Servít, František (1907). Eukleidovy Zaklady (Elementa) [Euclid's Elements] (PDF) (in Czech).
  • Sertöz, Ali Sinan (2019). Öklidin Elemanlari: Ciltli [Euclid's Elements] (in Turkish). Tübitak. ISBN .
  • Toussaint, Godfried (1993). "A new look at euclid's second proposition". The Mathematical Intelligencer. 15 (3): 12–24. doi:10.1007/BF03024252. ISSN 0343-6993. S2CID 26811463.
  • Waerden, Bartel Leendert (1975). Science awakening. Noordhoff International. ISBN .
  • Wilson, Nigel Guy (2006). Encyclopedia of Ancient Greece. Routledge.
  • Euklid (1999). Elementi I-VI. Translated by Hudoletnjak Grgić, Maja. KruZak. ISBN .

External links[edit]

  • Multilingual edition of Elementa in the Bibliotheca Polyglotta
  • Euclid (1997) [c. 300 BC]. David E. Joyce (ed.). "Elements". Retrieved 2006-08-30. In HTML with Java-based interactive figures.
  • Richard Fitzpatrick's bilingual edition (freely downloadable PDF, typeset in a two-column format with the original Greek beside a modern English translation; also available in print as ISBN 979-8589564587)
  • Heath's English translation (HTML, without the figures, public domain) (accessed February 4, 2010)
  • Oliver Byrne's 1847 edition (also hosted at– an unusual version by Oliver Byrne who used color rather than labels such as ABC (scanned page images, public domain)
  • Web adapted version of Byrne’s Euclid designed by Nicholas Rougeux
  • Video adaptation, animated and explained by Sandy Bultena, contains books I-VII.
  • The First Six Books of the Elements by John Casey and Euclid scanned by Project Gutenberg.
  • Reading Euclid – a course in how to read Euclid in the original Greek, with English translations and commentaries (HTML with figures)
  • Sir Thomas More's manuscript
  • Latin translation by Aethelhard of Bath
  • Euclid Elements – The original Greek text Greek HTML
  • Clay Mathematics Institute Historical Archive – The thirteen books of Euclid's Elements copied by Stephen the Clerk for Arethas of Patras, in Constantinople in 888 AD
  • Kitāb Taḥrīr uṣūl li-Ūqlīdis Arabic translation of the thirteen books of Euclid's Elements by Nasīr al-Dīn al-Ṭūsī. Published by Medici Oriental Press(also, Typographia Medicea). Facsimile hosted by Islamic Heritage Project.
  • Euclid's Elements Redux, an open textbook based on the Elements
  • 1607 Chinese translations reprinted as part of Siku Quanshu, or "Complete Library of the Four Treasuries."

Pages geometry book

‘Shape’ Makes Geometry Entertaining. Really, It Does.

Books of The Times

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“Girls can’t do Euclid: can they, sir?”

“The Mill on the Floss” contains one of George Eliot’s sharpest caricatures in the figure of the foul schoolmaster Stelling. About girls, he reassures his young charges: “They’ve a great deal of superficial cleverness; but they couldn’t go far into anything.”

Certainly not geometry, that maker of men. Stelling embodied British pedagogy at the time, with all its complacent sexism and emphasis on rote memorization. But as the emphasis shifted from students parroting proofs to forming their own, geometry remained exalted for its power to cultivate deductive reasoning, to toughen and refine the mind.

“I keep waiting for that to happen to me and it never has,” the mathematician Jordan Ellenberg confesses in his unreasonably entertaining new book, “Shape,” with its modest subtitle: “The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else.” In granular detail, he reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.

Before we begin: A moment of appreciation for the popular math writer who must operate with the same stealth, balletic improvisation and indomitable self-belief as someone trying to corner a particularly skittish and paranoid cat into the pet carrier. No sudden moves! Approach carefully; compliment liberally — precious reader, brilliant reader. Offer bribe and blandishment. Assure us it won’t hurt.

Ellenberg, a professor at the University of Wisconsin–Madison, is rather spectacular at this sort of thing. A seam in his narrative is a critique of how math, and especially geometry, has been taught. (His strategy for success in teaching is to employ more strategies; multiply approaches so students might find one that works for them.) He also takes a few well-aimed swipes at current depictions of the campus culture wars. The “cosseted” American college student might have launched a thousand Substacks, but have you heard of the “Conic Sections Rebellion”? Some 44 students, including the son of Vice President John C. Calhoun, were expelled from Yale in 1830, for refusing to take a geometry exam.

Explore the New York Times Book Review

Want to keep up with the latest and greatest in books? This is a good place to start.

Geometry occupies a peculiar place in the imagination. “There are people who hate it,” Ellenberg writes, “who tell me geometry was the moment math stopped making sense to them. Others tell me it was the only part of math that made sense to them. Geometry is the cilantro of math. Few are neutral.”

And yet, we are wired for it: “From the second we exit hollering from the womb we’re reckoning where things are and what they look like.”

You can give babies geometry tests. If you offer them pictures of pairs of shapes, most of them identical, but occasionally with one of the shapes reversed, babies will stare longer at the reversed shapes: “They know something’s going on, and their novelty-seeking minds strain toward it.” (Full disclosure: I was not able to replicate this finding. My subject proved recalcitrant and ate said card, offering a twist, perhaps, on Ellenberg’s notion that geometry is “primal, built into our bodies.”)

Those who drink the hallucinogenic ayahuasca report seeing two-dimensional patterns or throbbing, three-dimensional hexahedral cells. When the reasoning mind melts away, only shapes remain.

Geometry gives us a world unclad. “Euclid alone has looked on Beauty bare,” wrote Edna St. Vincent Millay. That feeling of mystical revelation — of a shimmering, underlying order that we can apprehend if we purify our perception — might explain the mutual affinity between poets and geometers. Dante mentions squaring the circle in “Paradiso.” Wordsworth repeatedly invokes Euclid. Many of the mathematicians cited in Ellenberg’s book wrote verse.

Ellenberg’s preference for deploying all possible teaching strategies gives “Shape” its hectic appeal; it’s stuffed with history, games, arguments, exercises. One entire lesson hinges on the question: How many holes are there in a pair of pants — one, two or three? Ellenberg puts footnotes to their only acceptable, nonacademic use, which is jokes.

If your grasp on the Virahanka-Fibonacci sequence is as hazy as mine, the biographical sections are honey. What a parade of beautiful minds, splendid eccentrics, catty squabbles. We meet the “mosquito man,” Sir Ronald Ross, whose study “The Logical Basis of the Sanitary Policy of Mosquito Reduction” became the foundation of the so-called random walk theory. And the polymathic Johann Benedict Listing, one of those miraculous dabblers that the 19th century seemed to churn out, who flitted from measuring the Earth’s magnetic field to sugar levels in the urine of diabetic patients.

Above all, Ellenberg borrows from one of the greatest math teachers — I refer, of course, to Mrs. Whatsit from “A Wrinkle in Time” — and embeds his approach in a narrative, not of the history of geometry but of our old association with it, of mathematics as a kind of mother tongue.

You might balk at delving into eigenvalues — “that strangely complicated number that governs the rate of geometric growth” — but I’ll bet you can recognize the sunny confidence of a C major chord and its individual notes. “The geometry was there in our bodies,” Ellenberg writes, “before we knew how to codify it on the page.”

For all Ellenberg’s wit and play (and his rightful admiration of some excellent 19th-century beards), the real work of “Shape” is in codifying that geometry on the page. Ellenberg butters you up to put you to work. I applied myself to my scrap paper with all the passionate ineptitude I remembered from my school days. The math he presents is serious and demanding and — this is key — shaping the world around us, from our understanding of the spread of Covid-19 to gerrymandering.

Wordsworth imagined that Euclidean geometry “wedded soul to soul in purest bond / Of reason, undisturbed by space or time.” To Ellenberg, geometry is not a reprieve from life but a force in it — and one that can be used for good, ill and for pleasures of its own. It binds and expands our notions of the world, the web of the real and the abstract.

“I prove a theorem,” the poet Rita Dove wrote, “and the house expands.”

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Pages Geometry Notebook Tutorial

Hair sticking out in different directions, all so sleepy. I wanted to get back into a warm bed and sleep soundly. Maybe I'll finish my dream. Grimaced to herself. The view is still the same.

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In self-flagellation. I assumed that if she spanked me, this tendency of mine might pass (strange conclusion, isn't it?). So we decided to give it a try. I suggested starting with the traditional belt (mine, Polish, made of genuine leather, medium width and rather hard).

Something more biting was also required, and then my perverted gaze fell on the cord from the tape recorder (Sharp).

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