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 1
... taken for granted that the perpendicular to the chord of an arc will meet the circle in two points . In some instances also the method of indirect demonstration is adopted , when the more satisfactory method of direct proof is available ...
... taken for granted that the perpendicular to the chord of an arc will meet the circle in two points . In some instances also the method of indirect demonstration is adopted , when the more satisfactory method of direct proof is available ...
Page 8
... taken in the diam . CE , the demonstration holds good only if G ' coincides with F ; should this not be the case , it is evident that G'CG'E .. G ' is not the cen . 2. The rigour of the reasoning would have been greatly promoted , if ...
... taken in the diam . CE , the demonstration holds good only if G ' coincides with F ; should this not be the case , it is evident that G'CG'E .. G ' is not the cen . 2. The rigour of the reasoning would have been greatly promoted , if ...
Page 9
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . CON . 1 , III . Pst . 1 & 2 . DEM . Def . 15 , I. 5 , I. The angles at the base of an isosc . A are equal to each other ; and if ...
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . CON . 1 , III . Pst . 1 & 2 . DEM . Def . 15 , I. 5 , I. The angles at the base of an isosc . A are equal to each other ; and if ...
Page 10
... taken & c . Q. E. D. COR . 1. - A st . line , A B , cannot cut the Oce of a in more points than two ; for , every st . line joining any two points in the Oce falls within the O , neither co - inciding with any other points in the Oce ...
... taken & c . Q. E. D. COR . 1. - A st . line , A B , cannot cut the Oce of a in more points than two ; for , every st . line joining any two points in the Oce falls within the O , neither co - inciding with any other points in the Oce ...
Page 17
... taken in the diameter of a circle , then , 1st , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and , 2nd , of ...
... taken in the diameter of a circle , then , 1st , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and , 2nd , of ...
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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