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
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal ... parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another and ...
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal ... parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another and ...
Página 38
... parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . PARALLELOGRAMS upon the same base , and between the same parallels , are equal to one another . * Let the parallelograms ABCD , EBCF be upon the same base BC , and ...
... parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . PARALLELOGRAMS upon the same base , and between the same parallels , are equal to one another . * Let the parallelograms ABCD , EBCF be upon the same base BC , and ...
Página 39
... parallelogram ; and it is equal ( 35. 1. ) to ABCD , because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the parallelogram EFGH is equal to the same EBCH ; therefore also the parallelogram ...
... parallelogram ; and it is equal ( 35. 1. ) to ABCD , because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the parallelogram EFGH is equal to the same EBCH ; therefore also the parallelogram ...
Página 40
... parallelogram EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the pa ... parallelogram ; and they are equal ( 36. 1. ) to one another , because they are upon equal bases BC , EF , and between ...
... parallelogram EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the pa ... parallelogram ; and they are equal ( 36. 1. ) to one another , because they are upon equal bases BC , EF , and between ...
Página 41
... parallelogram and triangle be upon the same base , and between the same parallels ; the parallelogram shall be double of the triangle . Let the parallelogram ABCD and the triangle EBC be upon F A DE the same base BC , and between the ...
... parallelogram and triangle be upon the same base , and between the same parallels ; the parallelogram shall be double of the triangle . Let the parallelogram ABCD and the triangle EBC be upon F A DE the same base BC , and between the ...
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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