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 100
Side 23
... common angle ABC , the remaining angle ABE is equal ( 3. Ax . ) to the re- maining angle ABD , the less to the greater , which is impossi- ble ; therefore BE is not in the same straight line with BC . And , in like manner , it may be ...
... common angle ABC , the remaining angle ABE is equal ( 3. Ax . ) to the re- maining angle ABD , the less to the greater , which is impossi- ble ; therefore BE is not in the same straight line with BC . And , in like manner , it may be ...
Side 33
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a ...
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a ...
Side 36
... common to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to the angle BCD ; therefore the base AC is equal ( 4. 1. ) to the base BD , and the triangle ABC to the triangle ...
... common to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ABC is equal to the angle BCD ; therefore the base AC is equal ( 4. 1. ) to the base BD , and the triangle ABC to the triangle ...
Side 37
... common to the two triangles , which is adjacent to their equal angles ; therefore their other sides shall be equal , each to each , and the third angle of the one to the third angle of the other , ( 26. 1. ) viz . the side AB to the ...
... common to the two triangles , which is adjacent to their equal angles ; therefore their other sides shall be equal , each to each , and the third angle of the one to the third angle of the other , ( 26. 1. ) viz . the side AB to the ...
Side 38
... common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two F A E D F A D E B C B C EA , AB are therefore equal to the two FD , DC , each to ...
... common ; therefore the whole , or the remainder AE , is equal ( 2. or 3. Ax . ) to the whole , or the remainder DF ; AB also is equal to DC ; and the two F A E D F A D E B C B C EA , AB are therefore equal to the two FD , DC , each to ...
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