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 7
... on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post . ) the second postulate ; ( Def . 3. ) the third definition , and so on . 29. The word , therefore , or hence , frequently OF GEOMETRY . BOOK I. 7.
... on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post . ) the second postulate ; ( Def . 3. ) the third definition , and so on . 29. The word , therefore , or hence , frequently OF GEOMETRY . BOOK I. 7.
Page 8
... hence , frequently occurs . To express either of these words , the sign .. is generally used . 30. If the quotients of two pairs of numbers , or quantities , are equal , the C quantities are said to be proportional : thus , if ; then ...
... hence , frequently occurs . To express either of these words , the sign .. is generally used . 30. If the quotients of two pairs of numbers , or quantities , are equal , the C quantities are said to be proportional : thus , if ; then ...
Page 15
... Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle ...
... Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle ...
Page 20
... hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the ...
... hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the ...
Page 28
... Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one ...
... Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one ...
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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 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
Popular passages
Page 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.
Page 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.
Page 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Page 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...
Page 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...
Page 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 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...