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 |
Dentro del libro
Resultados 1-5 de 100
Página 13
... straight line . Let AB be the given straight line ; it is required to ... BC is equal to BA : but it has been proved that CA is equal to AB ... BC are equal to one another ; and the triangle ABC is therefore equilateral , and it is ...
... straight line . Let AB be the given straight line ; it is required to ... BC is equal to BA : but it has been proved that CA is equal to AB ... BC are equal to one another ; and the triangle ABC is therefore equilateral , and it is ...
Página 14
... BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL ...
... BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL ...
Página 15
... BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ... straight line AB upon DE ; the point B shall coincide with the point E ... straight line AC is equal to DF : but the point B coincides with the point E ...
... BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ... straight line AB upon DE ; the point B shall coincide with the point E ... straight line AC is equal to DF : but the point B coincides with the point E ...
Página 18
... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E , and the B D G CE F straight line BC upon EF ; the point C shall also coincide with the point ...
... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E , and the B D G CE F straight line BC upon EF ; the point C shall also coincide with the point ...
Página 19
... BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall ... straight line AF bisects the angle BAC . Because AD is equal to AE , and AF ... straight line AF , which was to be done . PROP . X. PROB . B D E C To bisect a ...
... BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall ... straight line AF bisects the angle BAC . Because AD is equal to AE , and AF ... straight line AF , which was to be done . PROP . X. PROB . B D E C To bisect a ...
Otras ediciones - Ver todas
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