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 17
... fore , if two angles , & c . Q. E. D. B Cor . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are ...
... fore , if two angles , & c . Q. E. D. B Cor . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are ...
Side 21
... fore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible ; therefore two straight lines can- A not have a common segment . PROP . XII . PROB . E D B C C To draw a straight line perpendicular to a ...
... fore the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible ; therefore two straight lines can- A not have a common segment . PROP . XII . PROB . E D B C C To draw a straight line perpendicular to a ...
Side 29
... fore the base BC is equal ( 4. 1. ) to the base EG ; and because DG is equal to DF , the angle DFG is equal ( 5 . 1. ) to the angle DGF ; but the angle DGF is greater than the an- gle EGF ; therefore B E C G F the angle DFG is greater ...
... fore the base BC is equal ( 4. 1. ) to the base EG ; and because DG is equal to DF , the angle DFG is equal ( 5 . 1. ) to the angle DGF ; but the angle DGF is greater than the an- gle EGF ; therefore B E C G F the angle DFG is greater ...
Side 31
... fore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore AB is not ...
... fore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore AB is not ...
Side 34
... fore also BGH , GHD are equal to two right angles . Where- fore , if a straight line , & c . Q. E. D. PROP . XXX . THEOR . STRAIGHT lines which are parallel to the same straight line are parallel to one another . Let AB , CD , be each ...
... fore also BGH , GHD are equal to two right angles . Where- fore , if a straight line , & c . Q. E. D. PROP . XXX . THEOR . STRAIGHT lines which are parallel to the same straight line are parallel to one another . Let AB , CD , be each ...
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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