The Elements of Euclid |
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Page 155
... the whole is to the greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the base .. A Job c + Book VI . PROP . I. THEOR . See Note + ...
... the whole is to the greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the base .. A Job c + Book VI . PROP . I. THEOR . See Note + ...
Page 156
... altitude , viz.the perpendicular drawn front the point A to BD : then , as the base BC is to the base CD , so is the triangle ABC to the triangle ACD , and the paral- lelogram EC to the parallelogram CF. E A F Produce BD both ways to ...
... altitude , viz.the perpendicular drawn front the point A to BD : then , as the base BC is to the base CD , so is the triangle ABC to the triangle ACD , and the paral- lelogram EC to the parallelogram CF. E A F Produce BD both ways to ...
Page 157
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
Page 229
... altitude , the insisting straight lines of which are terminated in the same straight lines in the plane See Note . opposite to the base , are equal to one another . Book XI . See the figures below . a 28. OF EUCLID . 229.
... altitude , the insisting straight lines of which are terminated in the same straight lines in the plane See Note . opposite to the base , are equal to one another . Book XI . See the figures below . a 28. OF EUCLID . 229.
Page 230
... altitude , and let their insisting straight lines AF , AG , LM , LN be terminated in the same straight line FN , and CD , CE , BH , BK be terminated in the same straight line DK ; the solid AH is equal to the solid AK . D First , Let ...
... altitude , and let their insisting straight lines AF , AG , LM , LN be terminated in the same straight line FN , and CD , CE , BH , BK be terminated in the same straight line DK ; the solid AH is equal to the solid AK . D First , Let ...
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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