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 47
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . In ... AE D HF BG K C " Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is ...
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . In ... AE D HF BG K C " Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is ...
Página 49
... AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and 1. AF is the rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . 30. ) to AB ; and 2. CE is contained by AB , BC , for ...
... AE is equal to the rectangles AF , CE ; and AE is the square of AB ; and 1. AF is the rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . 30. ) to AB ; and 2. CE is contained by AB , BC , for ...
Página 59
... rectangle AB , BH , is equal to the square of AH . FG A HB E KD Produce GH to K. Then because the straight line AC is bisected in E , and produced to the point F , ( II . 6. ) 1. The rectangle CF , FA , together with the square of AE ...
... rectangle AB , BH , is equal to the square of AH . FG A HB E KD Produce GH to K. Then because the straight line AC is bisected in E , and produced to the point F , ( II . 6. ) 1. The rectangle CF , FA , together with the square of AE ...
Página 95
... rectangle contained by the segments of the other . Let the two straight lines AC , BD , within the circle ABCD , cut one another in the point E : the rectangle contained by AE , EC , is equal to the rectangle contained by BE , ED ...
... rectangle contained by the segments of the other . Let the two straight lines AC , BD , within the circle ABCD , cut one another in the point E : the rectangle contained by AE , EC , is equal to the rectangle contained by BE , ED ...
Página 96
... AE , EC , are equal to one another : and because the straight line BD is cut into two equal parts in the point F , and into two unequal parts in the point E , ( II . 5. ) 2. The rectangle ... AE , EF , are equal ( I. 47. ) to the square ...
... AE , EC , are equal to one another : and because the straight line BD is cut into two equal parts in the point F , and into two unequal parts in the point E , ( II . 5. ) 2. The rectangle ... AE , EF , are equal ( I. 47. ) to the square ...
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Términos y frases comunes
AC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double draw 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 THEOREM 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...