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 every parallelogram , any of the parallelograms about a diameter ... rectangle contained EUCLID'S ELEMENTS OF GEOMETRY. ...
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter ... rectangle contained EUCLID'S ELEMENTS OF GEOMETRY. ...
Página 48
Euclides Samuel A Good. A , BC , is equal to the rectangle contained by A , BD , together with that contained by A ... rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , by A , DE , and by A , EC ...
Euclides Samuel A Good. A , BC , is equal to the rectangle contained by A , BD , together with that contained by A ... rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , by A , DE , and by A , EC ...
Página 49
... 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 BE is equal to AB ; therefore 3. The rectangle contained by AB , AC , together with 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 BE is equal to AB ; therefore 3. The rectangle contained by AB , AC , together with the ...
Página 50
... rectangle contained by AC , CB . C B G H K D F E Upon AB describe ( I. 46. ) the square ADEB , and join BD ; and through draw ( I. 31. ) CGF parallel to AD or BE ; and through G draw HK parallel to AB or DE . And because CF is parallel ...
... rectangle contained by AC , CB . C B G H K D F E Upon AB describe ( I. 46. ) the square ADEB , and join BD ; and through draw ( I. 31. ) CGF parallel to AD or BE ; and through G draw HK parallel to AB or DE . And because CF is parallel ...
Página 51
... rectangle AC , CB ; wherefore 13 . 14. AG , GE , are equal to twice the rectangle AC , CB : and HF , CK , are the ... contained by the unequal parts , together with the square of the line between the points of section , is equal to the ...
... rectangle AC , CB ; wherefore 13 . 14. AG , GE , are equal to twice the rectangle AC , CB : and HF , CK , are the ... contained by the unequal parts , together with the square of the line between the points of section , is equal to the ...
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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...