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 7
... given circle . SOL . - Pst . 1. Let it be granted that a st . line may be drawn from any one point to any other point . 10 , I. To bisect a given finite st . line . 11 , I. To draw a st . line at rt.s to a given st . line from a given ...
... given circle . SOL . - Pst . 1. Let it be granted that a st . line may be drawn from any one point to any other point . 10 , I. To bisect a given finite st . line . 11 , I. To draw a st . line at rt.s to a given st . line from a given ...
Page 10
... 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 , nor meeting it except in the two given ...
... 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 , nor meeting it except in the two given ...
Page 11
... given line AB , take find D cen . of the O ; and join DA , DE , DB . D. 1 Def . 15 , I. 5 , I. in ADAB , DA = DB ; 2 ... st . line in only one point ; for if the st . line touched two points of the Oce the st . line would be drawn from ...
... given line AB , take find D cen . of the O ; and join DA , DE , DB . D. 1 Def . 15 , I. 5 , I. in ADAB , DA = DB ; 2 ... st . line in only one point ; for if the st . line touched two points of the Oce the st . line would be drawn from ...
Page 13
... Given a circle , ABC , to find its centre , as in the last figure . S. 1 ... st . line , to draw a circle . S. 1 Pst . 1. 10 , I. 2 11. I. 3 Cor . 3 ... given in Prop . 9 , III . K E IV . In Trigonometry we show 1st , by this PROP . III ...
... Given a circle , ABC , to find its centre , as in the last figure . S. 1 ... st . line , to draw a circle . S. 1 Pst . 1. 10 , I. 2 11. I. 3 Cor . 3 ... given in Prop . 9 , III . K E IV . In Trigonometry we show 1st , by this PROP . III ...
Page 17
... st . line FEB , meeting the Os in F cen . of F cen . of But FC • s E & B. ABC .. FC = FB ; CDE .. FC FB .. FE = FB ... given in a given line , to make a rectl . equal to a given rectl .. 3 , I. From the gr . of two given lines to cut off ...
... st . line FEB , meeting the Os in F cen . of F cen . of But FC • s E & B. ABC .. FC = FB ; CDE .. FC FB .. FE = FB ... given in a given line , to make a rectl . equal to a given rectl .. 3 , I. From the gr . of two given lines to cut off ...
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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