The Elements of Euclid |
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Page 119
... multiple of a less , when the greater is measured by the less , that is , when the ' greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
... multiple of a less , when the greater is measured by the less , that is , when the ' greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
Page 120
... 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 to have to the second a greater ratio than the third mag- nitude has to ...
... 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 to have to the second a greater ratio than the third mag- nitude has to ...
Page 123
... multiple of a greater magnitude is greater than the same multiple of a less .. IV . That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . 54 IF any ...
... multiple of a greater magnitude is greater than the same multiple of a less .. IV . That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . 54 IF any ...
Page 124
... multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third ...
... multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third ...
Page 125
... multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimul- tiples EF , GH be taken : then EF is the same multiple of B , that GH is of D. Because EF is the same multiple of A , that GH is of C , there ...
... multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimul- tiples EF , GH be taken : then EF is the same multiple of B , that GH is of D. Because EF is the same multiple of A , that GH is of C , there ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore