The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 39
... half of the parallelogram EBCA , because the diameter AB bisects it : and the triangle 34. L DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are * equal ; therefore the * 7 ...
... half of the parallelogram EBCA , because the diameter AB bisects it : and the triangle 34. L DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are * equal ; therefore the * 7 ...
Page 40
... 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. PROP . XXXIX . THEOR ...
... 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. PROP . XXXIX . THEOR ...
Page 53
... half the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D : the rectangle AD , DB , together with the square of CD , shall be equal to the square of CB . Ax ...
... half the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D : the rectangle AD , DB , together with the square of CD , shall be equal to the square of CB . Ax ...
Page 54
... half the line bi- sected , is equal to the square of the straight line which is made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D : the rectangle AD , DB , together with ...
... half the line bi- sected , is equal to the square of the straight line which is made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D : the rectangle AD , DB , together with ...
Page 58
... half of a right angle . For the same reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle . And because the angle GEF is half a right angle , and EGF a right angle , for it is * 29. 1 ...
... half of a right angle . For the same reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle . And because the angle GEF is half a right angle , and EGF a right angle , for it is * 29. 1 ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole