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 |
Inni boken
Resultat 6-10 av 53
Side 58
... half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares ... half a right angle ( 32. 1. ) : for the same reason , each of the angles CEB , EBC is half a right angle : therefore ...
... half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares ... half a right angle ( 32. 1. ) : for the same reason , each of the angles CEB , EBC is half a right angle : therefore ...
Side 59
... half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD is equal ( 6. 1. ) to the side DG : again , because EGF is half a right angle , and that the angle at F is a right angle , because it is equal ...
... half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD is equal ( 6. 1. ) to the side DG : again , because EGF is half a right angle , and that the angle at F is a right angle , because it is equal ...
Side 88
... half of the angle BGC , and the angle at D half of the angle EHF therefore the angle at A is equal to the angle at D. Wherefore , in equal circles , & c . Q. E. D. 1 PROP . XXVIII . THEOR . In equal circles. 88 BOOK III . THE ELEMENTS OF ...
... half of the angle BGC , and the angle at D half of the angle EHF therefore the angle at A is equal to the angle at D. Wherefore , in equal circles , & c . Q. E. D. 1 PROP . XXVIII . THEOR . In equal circles. 88 BOOK III . THE ELEMENTS OF ...
Side 107
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides . opposite to these are equal , viz . FG to GE in the same manner , it may be de- monstrated that GH , GK are each of them equal to FG or GE ; therefore F the ...
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides . opposite to these are equal , viz . FG to GE in the same manner , it may be de- monstrated that GH , GK are each of them equal to FG or GE ; therefore F the ...
Side 113
... half of the angle BCD , and CDF the half of CDE ; the angle FCD is equal to FDC ; wherefore the side CF is equal ( 6. 1. ) to the side FD : B A F E D in like manner it may be demonstrated that FB , FA , FE are each of them equal to FC ...
... half of the angle BCD , and CDF the half of CDE ; the angle FCD is equal to FDC ; wherefore the side CF is equal ( 6. 1. ) to the side FD : B A F E D in like manner it may be demonstrated that FB , FA , FE are each of them equal to FC ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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