The Elements of EuclidJohnson and Warner, 1811 - 518 Seiten |
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Seite vi
... similar solid " figures are those which are contained by similar planes of the same number and magnitude . ” Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and ...
... similar solid " figures are those which are contained by similar planes of the same number and magnitude . ” Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be demonstrated , and ...
Seite vii
... similar to one another , in the true sense of similarity received by all geometers ; and all · these propositions have , for these reasons , been insufficiently demonstrated since Theon's time hitherto . Besides , there are several ...
... similar to one another , in the true sense of similarity received by all geometers ; and all · these propositions have , for these reasons , been insufficiently demonstrated since Theon's time hitherto . Besides , there are several ...
Seite 68
... Similar segments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP . I. PROB . See Note . a 10. 1 . b 11. 1 . TO find the centre of a given circle . Let ABC be the given circle ; it is ...
... Similar segments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP . I. PROB . See Note . a 10. 1 . b 11. 1 . TO find the centre of a given circle . Let ABC be the given circle ; it is ...
Seite 87
... similar to the segment A D a 10. 3 . B ADB , and that similar segments of circles contain b equal an - b 11. def . R : ' gles ; the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible c . Therefore ...
... similar to the segment A D a 10. 3 . B ADB , and that similar segments of circles contain b equal an - b 11. def . R : ' gles ; the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible c . Therefore ...
Seite 88
... similar segments , & c . Q. E. D. ~ · a 23. 3 . See Note . a 10. 1 . b 11. 1 . c 6.1 . d 9. 3 . 23. 1 . £ 4.1 . PROP . XXV . PROB A SEGMENT of a circle being given , to describe . the circle of which it is the segment . Let ABC be the ...
... similar segments , & c . Q. E. D. ~ · a 23. 3 . See Note . a 10. 1 . b 11. 1 . c 6.1 . d 9. 3 . 23. 1 . £ 4.1 . PROP . XXV . PROB A SEGMENT of a circle being given , to describe . the circle of which it is the segment . Let ABC be the ...
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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