The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 36
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N.B. – A parallelogram is a four - sided figure , of which the opposite sides are ...
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N.B. – A parallelogram is a four - sided figure , of which the opposite sides are ...
Page 37
BC divides the parallelogram ACDB into two equal parts . Q. E. D. 2d and 3d ין * 34. 1 . PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the parallelograms ABCD ...
BC divides the parallelogram ACDB into two equal parts . Q. E. D. 2d and 3d ין * 34. 1 . PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the parallelograms ABCD ...
Page 38
FDC from the trapezium ABCF , and from the same trapezium take the triangle EAB , and the * 3 Ax . remainders * are equal ; that is , the parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same ...
FDC from the trapezium ABCF , and from the same trapezium take the triangle EAB , and the * 3 Ax . remainders * are equal ; that is , the parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same ...
Page 39
C draw CF parallel to BD : therefore each of the figures EBCA , DBCF is at parallelogram : Def . and EBCA is equal * to DBCF , because they 35.2 . - are upon the same base BC , and between the same parallels BC , EF ; and the triangle ...
C draw CF parallel to BD : therefore each of the figures EBCA , DBCF is at parallelogram : Def . and EBCA is equal * to DBCF , because they 35.2 . - are upon the same base BC , and between the same parallels BC , EF ; and the triangle ...
Page 40
is the half of the parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are * equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q. E. D. ' * 37 .
is the half of the parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are * equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q. E. D. ' * 37 .
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Common terms and phrases
altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole
Bibliographic information
| Title | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Author | Euclid |
| Editors | Robert Simson, Samuel Maynard |
| Translated by | Robert Simson |
| Publisher | Longman, Orme, Brown, Green, and Longmans, 1838 |
| Original from | University of Iowa |
| Digitized | 13 Jul 2015 |
| Length | 328 pages |
| Export Citation | BiBTeX EndNote RefMan |