## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |

### Dentro del libro

Resultados 1-5 de 19

Página 14

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**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 point in the same . Let AB be a given straight line , and C a ... Página 32

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**divided**into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And by the preceding proposition , ali the angles of these triangles are equal to twice as many ... Página 47

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**divided**into any number of parts , the rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several parts of the**divided**line . Let A and BC be two straight lines ; and let ... Página 48

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**divided**into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole line . Let the straight line AB be**divided**into any two parts in the point C ; the rectangle ... Página 49

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**divided**into any two parts , the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . Let the straight line AB be**divided**into any ...### Otras ediciones - Ver todas

### 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...