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 13
... BC is equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal to the same are equal to one another ; ( 1st Axiom . ) therefore CA is equal to CB ...
... BC is equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal to the same are equal to one another ; ( 1st Axiom . ) therefore CA is equal to CB ...
Página 14
... 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 has been ...
... 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 has been ...
Página 15
... equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the R angle ABC to the ...
... equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the R angle ABC to the ...
Página 18
... equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to ... 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 ...
... equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to ... 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 ...
Página 19
... BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different ...
... BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different ...
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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