The Elements of Euclid |
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Page 23
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line perpendicular to AB from the point C. Take any point Dupon the other side of AB , and from the centre C , at the distance CD ...
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line perpendicular to AB from the point C. Take any point Dupon the other side of AB , and from the centre C , at the distance CD ...
Page 26
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA ...
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA ...
Page 28
... Produce BA to the point D , and make AD equal to AC ; and join DC . ; to Because DA is equal to AC , the angle ADC is likewise equal ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the B ...
... Produce BA to the point D , and make AD equal to AC ; and join DC . ; to Because DA is equal to AC , the angle ADC is likewise equal ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the B ...
Page 34
... produced do not meet towards B , D. In like man- ner it may be demonstrat- ed that they do not meet towards A , C ; but those F D. straight lines which meet neither way , though produced ever so far , are parallel to one another . AB ...
... produced do not meet towards B , D. In like man- ner it may be demonstrat- ed that they do not meet towards A , C ; but those F D. straight lines which meet neither way , though produced ever so far , are parallel to one another . AB ...
Page 35
... produced ; therefore the straight lines AB , CD , if notes on produced far enough , shall meet ; but they never meet , since this propo- they are parallel by the hypothesis ; therefore the angle AGH is not unequal to the angle GHD ...
... produced ; therefore the straight lines AB , CD , if notes on produced far enough , shall meet ; but they never meet , since this propo- they are parallel by the hypothesis ; therefore the angle AGH is not unequal to the angle GHD ...
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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