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What people are saying - Write a reviewUser Review - Flag as inappropriate This book is missing pages 369-370 Related books
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Common terms and phrasesarea a medial base binomial straight line bisected circle ABCD circle EFGH commensurable in length commensurable in square cone cube cut in extreme cylinder decagon Deff diameter dodecahedron equilateral Eucl Euclid extreme and mean greater segment Hence icosahedron inscribed irrational straight line Lemma let the square magnitudes mean ratio measure medial area medial straight line medial whole parallelepipedal solids parallelogram pentagon perpendicular plane angles plane of reference polygon prism Proposition proved ratio triplicate rational and incommensurable rational area rational straight line rectangle AC rectangle contained right angles second apotome side similar Similarly sixth binomial solid angle solid CD sphere square number squares on AC straight lines commensurable surable theorem triangle twice the rectangle vertex whence Popular passagesPage 14 - Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out. the Page 262 - 4. A plane is at right angles to a plane when the straight lines drawn, in one of the planes, at right angles to the common section of the planes are at right angles to the remaining plane. 5. The inclination of a straight line to a plane is, Page 14 - than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude which will be less than the magnitude C. For C if multiplied Page 347 - Solid parallelepipeds contained by parallelograms equiangular to one another, each to each, that is, of which the solid angles are equal, each to each, have to one another the ratio compounded of the ratios of their sides. The Page 305 - a plane is at right angles to a plane, when the straight lines drawn, in one of the planes, at right angles to the common section of the planes are at right angles to the remaining plane. Page 28 - squares on straight lines incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides commensurable in length either. Page 297 - Also, from a point above a plane there can be but one perpendicular to that plane; for, if there could be two, they would be parallel to one another [xi. 6], which is absurd. Page 262 - 6. The inclination of a plane to a plane is the acute angle contained by the straight lines drawn at right angles to the common section at the same point, one in each of the planes. Page 26 - PROPOSITION 6. If two magnitudes have to one another the ratio which a number has to a number, the magnitudes will be commensurable. For let the two magnitudes A, B have to one another the ratio which the number D has to the number E Page 26 - For let A be divided into as many equal parts as there are units in D, and let C be equal to one of them ; and let F be made up of as many magnitudes equal to C as References to this bookFrom Google ScholarWhat Does It Mean To Say That Logic Is Formal?John Gordon MacFarlane - 2000 References from web pagesHeath: <i>The thirteen books of Euclid's Elements</i> Preface JSTOR: The Thirteen Books of Euclid's Elements avaxhome -> ebooks -> Science -> Mathematics -> The Thirteen Books ... Euclid & The Thirteen Books of Euclid's Elements Discussion Deck The Thirteen Books of Euclid's Elements - Timeline Index The thirteen books of Euclid's Elements ; v. 3. Books X-XIII and ... Euclid's Elements, Euclid The 47th Problem of Euclid | Masonic significance Euclid - Wikipedia, the free encyclopedia Did Euclid Need the Euclidean Algorithm to Prove Unique Factorization? Bibliographic information
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