The Elements of Euclid |
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Page 39
... parallelograms are equal to one another , and the diameter bisects them that is , divides them into two equal parts ... parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ...
... parallelograms are equal to one another , and the diameter bisects them that is , divides them into two equal parts ... parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ...
Page 40
... parallelograms ABCD , EPCF , be not terminated in the same point ; then , be- cause ABCD is a parallelogram , AD is equal a to BC ; for the same reason EF is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the ...
... parallelograms ABCD , EPCF , be not terminated in the same point ; then , be- cause ABCD is a parallelogram , AD is equal a to BC ; for the same reason EF is equal to BC ; wherefore AD is equal to EF ; and DE is common ; therefore the ...
Page 41
... parallelogram ; and it is equal to * 35. 1 . ABCD , because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the parallelogram EFGH is equal to the same EBCH : therefore also the paral ...
... parallelogram ; and it is equal to * 35. 1 . ABCD , because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the parallelogram EFGH is equal to the same EBCH : therefore also the paral ...
Page 42
... parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are equal ; therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c . Q. E. D. c . 34. 1 . d 7. Ax . a 31. 1 . b 36. 1 ...
... parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are equal ; therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c . Q. E. D. c . 34. 1 . d 7. Ax . a 31. 1 . b 36. 1 ...
Page 43
... . Q. E. D. PROP . XLI . THEOR . IF a parallelogram and triangle be upon the same base , and between the same parallels ; the parallel p- gram shall be double of the triangle . b 38. 1 , Book I. a 37. 1 . b34 . 1 . OF EUCLID . 43.
... . Q. E. D. PROP . XLI . THEOR . IF a parallelogram and triangle be upon the same base , and between the same parallels ; the parallel p- gram shall be double of the triangle . b 38. 1 , Book I. a 37. 1 . b34 . 1 . OF EUCLID . 43.
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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