## 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 Sperical TrigonometryW.E. Dean, 1844 - 317 páginas |

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**equivalent**to the sum of any number of squares ; for a**similar**construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square ... Página 62

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**Similar**segments of a circle , are those in which the angles are**equal**, or which contain**equal**an- gles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ... Página 76

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**equal**to the interior opposite angle . COR . 2. It follows , likewise , that a quadrilateral , of which the op- posite angles are not**equal**to two right angles , cannot be inscribed in a circle . PROP . XXIII . THEOR . Upon the**same**... Página 78

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**equal**to the angle at D , the segment BAC is**similar**( 9. def . 3. ) to the segment EDF ; and they are upon**equal**straight lines BC , EF ; but**similar**segments of circles upon**equal**straight lines are**equal**( 24. 3. ) to one another ... Página 87

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**equal**. For**similar**reasons FB , FC , are**equal**; hence the points A , B , C , are all equally distant from the point F , and consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that ...### Otras ediciones - Ver todas

### Términos y frases comunes

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder 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 magnitudes meet multiple 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

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Página 95 - 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 68 - THE angles in the same segment of a circle are equal to one another...

Página 23 - 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.

Página 74 - 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.

Página 78 - 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 9 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Página 75 - If a straight line touch a circle, and from the point of contact a...

Página 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Página 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Página 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.