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 13
... base BC coincide with the base EF , but the sides BA , CA , do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles ...
... base BC coincide with the base EF , but the sides BA , CA , do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles ...
Página 14
... base AD is equal to the base DB ; 4. The straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given ...
... base AD is equal to the base DB ; 4. The straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given ...
Página 15
... base DF is equal to the base EF ; The angle DCF is equal to the angle ECF ; and they are adjacent angles . But when the adjacent angles which one straight line makes with another straight line are equal to one another , each of them is ...
... base DF is equal to the base EF ; The angle DCF is equal to the angle ECF ; and they are adjacent angles . But when the adjacent angles which one straight line makes with another straight line are equal to one another , each of them is ...
Página 16
... base CF is equal to the base CG ; 3. The angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing on another straight line makes the adjacent angles equal to one another , each of them is a ...
... base CF is equal to the base CG ; 3. The angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing on another straight line makes the adjacent angles equal to one another , each of them is a ...
Página 19
... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite : wherefore , 4 . The angle BAE is equal to the angle ...
... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite : wherefore , 4 . The angle BAE is equal to the angle ...
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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...