The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 39
are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the diameter AB bisects * it : and the triangle * 34 . L DBC is the half of the parallelogram DBCF ...
are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the diameter AB bisects * it : and the triangle * 34 . L DBC is the half of the parallelogram DBCF ...
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 .
Page 53
If a straight line be divided into two equal parts , and also into two unequal parts ; the rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half ...
If a straight line be divided into two equal parts , and also into two unequal parts ; the rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half ...
Page 54
If a straight line be bisected , and produced to any point ; the rectangle contained by the whole ' line thus produced , and the part of it produced , together with the square of half the line bi- . sected , is equal to the square of ...
If a straight line be bisected , and produced to any point ; the rectangle contained by the whole ' line thus produced , and the part of it produced , together with the square of half the line bi- . sected , is equal to the square of ...
Page 58
If a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line , and of the square of the line between the points of section .
If a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line , and of the square of the line between the points of section .
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
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 |