## 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 TrigonometryJ.P. Lippincott & Company, 1856 - 318 sider |

### Fra bogen

Resultater 1-5 af 41

Side 33

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**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 ... Side 34

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**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 ... Side 36

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**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 ... Side 37

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**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 ... Side 39

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**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 ...### Andre udgaver - Se alle

### Almindelige termer og sætninger

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle BCD base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw 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 line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB produced PROP proportional proposition 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 AC tangent THEOR touches the circle triangle ABC triangle DEF wherefore

### Populære passager

Side 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.

Side 81 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.

Side 14 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 19 - The angles which one straight line makes with another upon one side uf it, are, either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.

Side 52 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C. Then the squares on AB, BC shall be equal to twice the rectangle AB, BC, together with the square on A C.

Side 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 242 - 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.

Side 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 119 - Reciprocal figures, viz. triangles and parallelograms, " are such as have their sides about two of their " angles proportionals in such a manner, that a side

Side 72 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...