The Elements of Euclid |
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Page 119
... equimultiples whatsoever of the first and third being ta- ken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that ...
... equimultiples whatsoever of the first and third being ta- ken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that ...
Page 120
... 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 122
... EQUIMULTIPLES of the saine , or of equal magnitudes , are equal to one another . 4. Prop . lib . 2. Archimedis de spliƦra et cylindro . II . Those magnitudes of which the same , or 122 THE ELEMENTS.
... EQUIMULTIPLES of the saine , or of equal magnitudes , are equal to one another . 4. Prop . lib . 2. Archimedis de spliƦra et cylindro . II . Those magnitudes of which the same , or 122 THE ELEMENTS.
Page 123
Euclid Robert Simson. II . Those magnitudes of which the same , or equal magnitudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less .. IV . That magnitude ...
Euclid Robert Simson. II . Those magnitudes of which the same , or equal magnitudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less .. IV . That magnitude ...
Page 125
... equimultiples , these shall be equimul- tiples , 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 equimul- tiples ...
... equimultiples , these shall be equimul- tiples , 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 equimul- tiples ...
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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