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 76
Euclides Samuel A Good. PROP . XIII . THEOREM . One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more points ...
Euclides Samuel A Good. PROP . XIII . THEOREM . One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more points ...
Página 80
... circle , as AC ; and draw DC to the point C where it meets the circumference . And because DA is equal ( I. Def . 15 ... touches the circle ( III . Def . 2. ) ; and 80 EUCLID'S ELEMENTS .
... circle , as AC ; and draw DC to the point C where it meets the circumference . And because DA is equal ( I. Def . 15 ... touches the circle ( III . Def . 2. ) ; and 80 EUCLID'S ELEMENTS .
Página 81
... touches it only in one point , because , if it did meet the circle in two , it would fall within it ( III . 2. ) . " Also it is evident that there can be but one straight line which touches the circle in the same point . " PROP . XVII ...
... touches it only in one point , because , if it did meet the circle in two , it would fall within it ( III . 2. ) . " Also it is evident that there can be but one straight line which touches the circle in the same point . " PROP . XVII ...
Página 82
... touches a circle , the straight line drawn from the centre to the point of contact , shall be perpendicular to the line touching the circle . Let the straight line DE touch the circle ABC in the point C ; take ( III . 1. ) the centre F ...
... touches a circle , the straight line drawn from the centre to the point of contact , shall be perpendicular to the line touching the circle . Let the straight line DE touch the circle ABC in the point C ; take ( III . 1. ) the centre F ...
Página 93
... touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line from the point of contact B , ( III . 19. ) 1. The centre of the circle ABCD is in BA ; therefore ( III . 31. ) 2. The angle ADB in a ...
... touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line from the point of contact B , ( III . 19. ) 1. The centre of the circle ABCD is in BA ; therefore ( III . 31. ) 2. The angle ADB in a ...
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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...