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 páginas |
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Página 37
... AC , BD , and makes the alternate angles ACB , CBD equal to one another , AC is paral- lel ( 27. 1. ) to BD ; and it ... parallelogram is a four sided figure , of which the opposite sides are parallel ; and the diameter is the straight line ...
... AC , BD , and makes the alternate angles ACB , CBD equal to one another , AC is paral- lel ( 27. 1. ) to BD ; and it ... parallelogram is a four sided figure , of which the opposite sides are parallel ; and the diameter is the straight line ...
Página 42
... parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , be- cause they are upon the same base BC , and between the same parallels BC , AE . But the parallelogram ABCD ...
... parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , be- cause they are upon the same base BC , and between the same parallels BC , AE . But the parallelogram ABCD ...
Página 43
... parallelogram , of which the diameter is AC , and EH , FG the parallelograms about AC , that is , through which AC passes , and BK , KD the other parallelograms which make up the E whole figure ABCD , which are therefore called the ...
... parallelogram , of which the diameter is AC , and EH , FG the parallelograms about AC , that is , through which AC passes , and BK , KD the other parallelograms which make up the E whole figure ABCD , which are therefore called the ...
Página 46
... AC at right angles to AB ; and make ( 3. 1. ) AD equal to ÁB , and through the point D draw DE parallel ( 31. 1. ) to AB , and through B draw BE pa- rallel to AD ; therefore ADEB is a parallelogram : whence AB is equal ( 34. 1. ) to DE ...
... AC at right angles to AB ; and make ( 3. 1. ) AD equal to ÁB , and through the point D draw DE parallel ( 31. 1. ) to AB , and through B draw BE pa- rallel to AD ; therefore ADEB is a parallelogram : whence AB is equal ( 34. 1. ) to DE ...
Página 47
... parallel to BD or CE , and join AD , FC : then , because each of the angles BAC , BAG , is a right angle , ( 30. def . ) the two straight lines AC , AG upon the opposite sides of AB , make with it at the point A the adjacent angles ...
... parallel to BD or CE , and join AD , FC : then , because each of the angles BAC , BAG , is a right angle , ( 30. def . ) the two straight lines AC , AG upon the opposite sides of AB , make with it at the point A the adjacent angles ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
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