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 xii
Euclides Henry Green. pos .. .position . prod . ... produce , produced . ... propl . .proportional . pt . .part . qu . ang ... quadrangular . qu . lat . rad . rat . recip . rect . rectl . rectr .. .quadrilateral . ... radius . ... .ratio ...
Euclides Henry Green. pos .. .position . prod . ... produce , produced . ... propl . .proportional . pt . .part . qu . ang ... quadrangular . qu . lat . rad . rat . recip . rect . rectl . rectr .. .quadrilateral . ... radius . ... .ratio ...
Page 3
... produced does not cut it ; as AB tan- gent to EFC in C. The point in which the straight line meets the circle is the point of contact ; the straight line " does not cut , " i . e . does not pass into the circle . A Secant is a straight ...
... produced does not cut it ; as AB tan- gent to EFC in C. The point in which the straight line meets the circle is the point of contact ; the straight line " does not cut , " i . e . does not pass into the circle . A Secant is a straight ...
Page 7
... produced to any length in a st . line . DEM . - Def . 15 , I. A is a plane figure contained by one line , which is called the circumference , and is such that all st . lines drawn from a certain point within the figure to the Oce are ...
... produced to any length in a st . line . DEM . - Def . 15 , I. A is a plane figure contained by one line , which is called the circumference , and is such that all st . lines drawn from a certain point within the figure to the Oce are ...
Page 8
... produced indefinitely in both directions , will meet the in two points , and not in more ; and every point of the line between these two points of intersection will be within the O , and every point beyond them without it . LARDNER'S ...
... produced indefinitely in both directions , will meet the in two points , and not in more ; and every point of the line between these two points of intersection will be within the O , and every point beyond them without it . LARDNER'S ...
Page 9
... produced , the s on the other side of the base shall be equal . 16 , I. If one side of a △ be produced the ext . is greater than either of the int . opp . angles . 19 , 1. The gr . of every A is subtended by the gr . side , or has the ...
... produced , the s on the other side of the base shall be equal . 16 , I. If one side of a △ be produced the ext . is greater than either of the int . opp . angles . 19 , 1. The gr . of every A is subtended by the gr . side , or has the ...
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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
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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.
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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