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, 1855 - 318 sider |
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Resultater 1-5 af 68
Side 12
... triangle upon a given finite straight line . Let AB be the given straight ... Definition ) to AB ; and because the point B is the centre of the cir- cle ACE ... Def . ) to BG ; and because D is the centre of the circle GKL , DL is equal ...
... triangle upon a given finite straight line . Let AB be the given straight ... Definition ) to AB ; and because the point B is the centre of the cir- cle ACE ... Def . ) to BG ; and because D is the centre of the circle GKL , DL is equal ...
Side 13
... triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . * Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF ...
... triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . * Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF ...
Side 14
... triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are ... DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the one equal to two sides ...
... triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are ... DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the one equal to two sides ...
Side 16
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to ... DEF be two triangles having the two sides AB , AC , equal to the two sides ... triangle ABC be applied to the triangle DEF , so that the point B be on E ...
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to ... DEF be two triangles having the two sides AB , AC , equal to the two sides ... triangle ABC be applied to the triangle DEF , so that the point B be on E ...
Side 17
... triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but ...
... triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but ...
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Almindelige termer og sætninger
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 line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane 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 spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære passager
Side 41 - 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 70 - 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.
Side 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Side 91 - 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...
Side 273 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...