The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |
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Page 117
... equi- multiples whatsoever of the second and fourth ; if the multi- ple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal to that ...
... equi- multiples whatsoever of the second and fourth ; if the multi- ple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal to that ...
Page 118
... equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said ...
... equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said ...
Page 121
... equal magnitudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same mul- tiple of a less . IV . That magnitude of which a multiple is greater than the same multiple of another ...
... equal magnitudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same mul- tiple of a less . IV . That magnitude of which a multiple is greater than the same multiple of another ...
Page 123
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF ...
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF ...
Page 124
... equimultiples of the second and fourth , viz . the equimultiple of the first shall have the same ratio to that of ... equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H : then E has the same ratio to G , which ...
... equimultiples of the second and fourth , viz . the equimultiple of the first shall have the same ratio to that of ... equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H : then E has the same ratio to G , which ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore