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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Side 13
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ... angles contained by those sides equal to one another , their bases , or third sides , shall be equal ; and the areas of the ...
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ... angles contained by those sides equal to one another , their bases , or third sides , shall be equal ; and the areas of the ...
Side 14
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to ...
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to ...
Side 15
... equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which ...
... equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which ...
Side 16
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much ...
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much ...
Side 17
... sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the ...
... sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the ...
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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...