The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 26
... angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side ... BAC . Produce BD to E ; and because two sides of a triangle are greater than the third side , the two sides BA , AE of the tri ...
... angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side ... BAC . Produce BD to E ; and because two sides of a triangle are greater than the third side , the two sides BA , AE of the tri ...
Side 29
... angle BAC greater than the angle EDF ; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line DE , make ( 23. 1. ) the ...
... angle BAC greater than the angle EDF ; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line DE , make ( 23. 1. ) the ...
Side 30
... angle BAC is not less than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. B C E F PROP . XXVI . THEOR . : Ir two ...
... angle BAC is not less than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. B C E F PROP . XXVI . THEOR . : Ir two ...
Side 31
... angle GBC is equal to the angle DEF ; therefore the base GC is equal ( 4. 1. ) to the base DF , and the tri- angle ... BAC to the third an- gle EDF . B D HCE F Next , let the sides which are opposite to A equal angles in each tri- angle ...
... angle GBC is equal to the angle DEF ; therefore the base GC is equal ( 4. 1. ) to the base DF , and the tri- angle ... BAC to the third an- gle EDF . B D HCE F Next , let the sides which are opposite to A equal angles in each tri- angle ...
Side 35
... angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal ... BAC , ACE are equal ( 29. 1. ) Again ; because A is parallel to CE , and BD falls upon them , the ex- terior angle ECD ...
... angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal ... BAC , ACE are equal ( 29. 1. ) Again ; because A is parallel to CE , and BD falls upon them , the ex- terior angle ECD ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore