The Elements of Euclid |
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Page vii
... reasons , been insufficiently demonstrated since Theon's time hitherto . Besides , there are several other things which have nothing of Euclid's accura- cy , 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 accura- cy , and which plainly show , that his Elements have been much corrupted by ...
Page 29
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angie 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 greater than the angie CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from ...
Page 40
... reason EF is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the whole , or the re- 2. or 3. Ax . mainder AE , is equal to the whole , or the remainder DF ; AB also is equal to DC ; and the two EA , AB are ...
... reason EF is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the whole , or the re- 2. or 3. Ax . mainder AE , is equal to the whole , or the remainder DF ; AB also is equal to DC ; and the two EA , AB are ...
Page 41
... reason , the parallelogram EFGH is equal to the same EBCH : therefore also the paral- lelogram ABCD is equal to EFGH . Wherefore parallelo- grams , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the ...
... reason , the parallelogram EFGH is equal to the same EBCH : therefore also the paral- lelogram ABCD is equal to EFGH . Wherefore parallelo- grams , & c . Q. E. D. PROP . XXXVII . THEOR . TRIANGLES upon the same base , and between the ...
Page 45
... 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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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