Elements of Geometry: Containing the First Six Books of Euclid with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical Trigonometry |
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Page 33
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallelo- A 5 OF GEOMETRY . BOOK I. 33 Th. 32.), and the opposite ...
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallelo- A 5 OF GEOMETRY . BOOK I. 33 Th. 32.), and the opposite ...
Page 34
... ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 34. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is com- mon ; therefore ...
... ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 34. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. Ax . ) to EF ; and DE is com- mon ; therefore ...
Page 36
... ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ...
... ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ...
Page 37
... ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD , and are therefore ...
... ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD , and are therefore ...
Page 39
... ABCD is equal to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , hav- ing the angle FKM equal to the given angle E. COR . From this it is manifest how to a ...
... ABCD is equal to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equal to the given rectilineal figure ABCD , hav- ing the angle FKM equal to the given angle E. COR . From this it is manifest how to a ...
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Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Page 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Page 11 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Page 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Page 84 - 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.
Page 80 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 22 - Any two sides of a triangle are together greater than the third side.
Page 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.