The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 26
... half of the parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it : but the halves of equal things are equal ( 7 ax ...
... half of the parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it : but the halves of equal things are equal ( 7 ax ...
Σελίδα 33
... half of the angle into the same number of equal angles . 6. Given the base , one of the angles at the base , and the sum of the other two sides , to construct the triangle . 7. To find a point in a triangle equidistant from the three ...
... half of the angle into the same number of equal angles . 6. Given the base , one of the angles at the base , and the sum of the other two sides , to construct the triangle . 7. To find a point in a triangle equidistant from the three ...
Σελίδα 34
... half of the vertical angle , according as the triangle is right , obtuse , or acute - angled . 22. If the vertical angle of an isosceles triangle be bisected , the bisecting line will bisect the base , and be perpendicular to it . 23 ...
... half of the vertical angle , according as the triangle is right , obtuse , or acute - angled . 22. If the vertical angle of an isosceles triangle be bisected , the bisecting line will bisect the base , and be perpendicular to it . 23 ...
Σελίδα 37
... of the line between the points of section , is equal to the square of 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 ; BOOK II . PROPS . IV . , V. 37.
... of the line between the points of section , is equal to the square of 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 ; BOOK II . PROPS . IV . , V. 37.
Σελίδα 38
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . LET the straight line a b be bisected in c , and produced to the point d ; the rectangle ad , db , together with ...
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . LET the straight line a b be bisected in c , and produced to the point d ; the rectangle ad , db , together with ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle