The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Página 34
... whole angle ABD is equal to the whole angle ACD ; and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter bisects them ...
... whole angle ABD is equal to the whole angle ACD ; and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another . Also , their diameter bisects them ...
Página 35
... whole , or the remainder , AE is equal to the whole , or the remainder , DF ; AB also is equal ( I. 34. ) to DC ; and the two EA , AB , are therefore equal to the two FD , DC , each to each ; and the exterior angle FDC is equal ( I. 29 ...
... whole , or the remainder , AE is equal to the whole , or the remainder , DF ; AB also is equal ( I. 34. ) to DC ; and the two EA , AB , are therefore equal to the two FD , DC , each to each ; and the exterior angle FDC is equal ( I. 29 ...
Página 40
... whole triangle ABC is equal to the whole ADC ; therefore 5. The remaining complement BK is equal to the remaining complement KD . Wherefore , the complements , & c . Q.E.D. PROP . XLIV . - PROBLEM . To a given 40 EUCLID'S ELEMENTS .
... whole triangle ABC is equal to the whole ADC ; therefore 5. The remaining complement BK is equal to the remaining complement KD . Wherefore , the complements , & c . Q.E.D. PROP . XLIV . - PROBLEM . To a given 40 EUCLID'S ELEMENTS .
Página 43
... whole rectilineal figure ABCD is equal to the whole parallelogram KFLM . Therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Which was to be ...
... whole rectilineal figure ABCD is equal to the whole parallelogram KFLM . Therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Which was to be ...
Página 44
... whole angle DBA is equal to the whole FBC . And because the two sides AB , BD , are 44 EUCLID'S ELEMENTS .
... whole angle DBA is equal to the whole FBC . And because the two sides AB , BD , are 44 EUCLID'S ELEMENTS .
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Términos y frases comunes
ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle
Pasajes populares
Página 26 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Página 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Página 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Página 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 7 - AB; but things which are equal to the same are equal to one another...
Página 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Página 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Página 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 52 - 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...