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 10
... sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ... BC ' is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their ...
... sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ... BC ' is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their ...
Página 11
... side of the base . Therefore the angles at the base , & c . Q.E.D. COROLLARY . - Hence every equilateral triangle is ... BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ; and the angle DBC is ...
... side of the base . Therefore the angles at the base , & c . Q.E.D. COROLLARY . - Hence every equilateral triangle is ... BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ; and the angle DBC is ...
Página 13
... BC equal to the base EF . The angle BAC is equal to the angle EDF ... side of it , there can be two triangles that have their sides which are ... BC coincide with the base EF , the sides BA , AC , cannot but coincide with the sides ED ...
... BC equal to the base EF . The angle BAC is equal to the angle EDF ... side of it , there can be two triangles that have their sides which are ... BC coincide with the base EF , the sides BA , AC , cannot but coincide with the sides ED ...
Página 18
... side of it , ( I. 13. ) 1. The angles ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD ... BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD ...
... side of it , ( I. 13. ) 1. The angles ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD ... BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD ...
Página 19
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles СВА , ВАС ... side BC be bisected , it may be demonstrated that the angle BCG that is ( I. 15. ) 6 . The angle ACD is greater than ...
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles СВА , ВАС ... side BC be bisected , it may be demonstrated that the angle BCG that is ( I. 15. ) 6 . The angle ACD is greater than ...
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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...