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 9
... reasons , been insufficiently demonstrated since Theon's time hitherto . Besides , there are several other things , which have nothing of Euclid's accuracy , and which plainly show , that his Elements have been much corrupted by ...
... reasons , been insufficiently demonstrated since Theon's time hitherto . Besides , there are several other things , which have nothing of Euclid's accuracy , and which plainly show , that his Elements have been much corrupted by ...
Side 27
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is great- er than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is great- er than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Side 38
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two ...
... reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two ...
Side 39
... reason , the parallelogram EFGH is equal to the same EBCH ; therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
... reason , the parallelogram EFGH is equal to the same EBCH ; therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the same ...
Side 43
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
... reason , the triangle KGC is equal to the triangle KFC : then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK , together with the triangle KGC , is equal to the triangle AHK ...
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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