The Elements of EuclidJohnson and Warner, 1811 - 518 Seiten |
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Seite 39
... parallelogram is a four sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides ...
... parallelogram is a four sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides ...
Seite 40
... parallelogram If the sides AD , DF of the paral- A lelograms ABCD , DBCF opposite to the base BC be terminated in the same point D ; it is plain that each of the parallelograms is double of the trian- gle BDC ; and they are therefore ...
... parallelogram If the sides AD , DF of the paral- A lelograms ABCD , DBCF opposite to the base BC be terminated in the same point D ; it is plain that each of the parallelograms is double of the trian- gle BDC ; and they are therefore ...
Seite 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 ...
Seite 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 ...
Seite 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