Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations in Euclid, part ii., with illustr. [&c.] by H. Green1861 |
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Page ix
... ratio . : = : equality of ratios . ::: proportion . : : : Numbers or Quantities in Progression The signs > , » , < , < , between ratios , as A : B > C : D , or A : BC : D , or A : B < C : D , or A : BC : D , denote that the one ratio is ...
... ratio . : = : equality of ratios . ::: proportion . : : : Numbers or Quantities in Progression The signs > , » , < , < , between ratios , as A : B > C : D , or A : BC : D , or A : B < C : D , or A : BC : D , denote that the one ratio is ...
Page 123
... ratio ( 11 , II . ) the greater segment , CD , will be the side of the decagon inscribed in that circle . Hence , PROB . 1 .--- To find the side of an inscribed decagon , when the rad . , CA , of a circle is given . By 11 , II ...
... ratio ( 11 , II . ) the greater segment , CD , will be the side of the decagon inscribed in that circle . Hence , PROB . 1 .--- To find the side of an inscribed decagon , when the rad . , CA , of a circle is given . By 11 , II ...
Page 127
... ratio of the circumference of a circle to its diameter . By forming Polygons of any number of sides that are successive bisections of the original 6 , as 12 , 24 , 48 , & c . , we obtain the apothem , i . e . , the perpendicular from ...
... ratio of the circumference of a circle to its diameter . By forming Polygons of any number of sides that are successive bisections of the original 6 , as 12 , 24 , 48 , & c . , we obtain the apothem , i . e . , the perpendicular from ...
Page 142
... Ratio ; the ratio , measured by the difference is named an arithmetical ratio , —that measured by the quotient , - —a geometrical ratio . Proportion is applied , either to an identity of difference between three or more numbers , as 12 ...
... Ratio ; the ratio , measured by the difference is named an arithmetical ratio , —that measured by the quotient , - —a geometrical ratio . Proportion is applied , either to an identity of difference between three or more numbers , as 12 ...
Page 141
... RATIO , or mode of estimating the relative lengths of lines and the magnitudes of figures , and the proportion , or ... Ratios , and the setting forth of proportions , rest so entirely on a numerical basis , that to a very high degree ...
... RATIO , or mode of estimating the relative lengths of lines and the magnitudes of figures , and the proportion , or ... Ratios , and the setting forth of proportions , rest so entirely on a numerical basis , that to a very high degree ...
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Euclid's Plane Geometry, Books III.-VI., Practically Applied; Or, Gradations ... Euclides No preview available - 2016 |
Common terms and phrases
ABCD Antecs Arith base bisected centre chord circumference circumscribed compd Conc contained decagon desc diam diameter distance divided draw drawn equiangular equims equimultiples Euclid extreme four magnitudes fourth Geometry given circle given line given st greater hypotenuse inscribed isosc join less mean measure multiple parallel parallelogram pentagon perp Plane Geometry polygon PROB Prop propl proportional proposition Quæs radius ratio compounded rect rectangle rectil rectilineal figure regular polygon Remk segments semic semiperimeter sides similar square star-shaped polygon straight line tang tangent third touch triangle vertex
Popular passages
Page 7 - If two triangles have two sides of the one equal to two sides of the...
Page 151 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...
Page 81 - 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.
Page 85 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Page 310 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 11 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Page 33 - 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...
Page 156 - XIII. Permutando, or alternando, by permutation, or alternately; this word is used when there are four proportionals, and it is inferred, that the first has the same ratio to the third, which the second has to the ,fourth; or that the first is to the third, as the second to the fourth; as is shown in the 16th prop.
Page 219 - If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually cited by the words "ex sequali,
Page 216 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words