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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Seite 3
... Equal circles are those of which the diameters are equal , or , from the centres of which the straight lines to the circumferences are equal . The criterion of the equality of circles is that their diameters or their radii are equal ...
... Equal circles are those of which the diameters are equal , or , from the centres of which the straight lines to the circumferences are equal . The criterion of the equality of circles is that their diameters or their radii are equal ...
Seite 6
... equal when they have equal radii and equal angles ; for by superposition their boun- daries coincide in every respect . Certain Sectors of a definite size are known by definite names ; as the Quadrant , a sector of which the arc is 90 ...
... equal when they have equal radii and equal angles ; for by superposition their boun- daries coincide in every respect . Certain Sectors of a definite size are known by definite names ; as the Quadrant , a sector of which the arc is 90 ...
Seite 7
... equal to one another . 8 , I. If two As have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by the two sides of the one , shall be equal to the ...
... equal to one another . 8 , I. If two As have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by the two sides of the one , shall be equal to the ...
Seite 9
... equal to each other ; and if the equal sides be 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 ...
... equal to each other ; and if the equal sides be 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 ...
Seite 11
... equal to two s of the other , each to each , and one side equal to one side , viz . , either the sides adj . to the equals in each , or the sides opp . to them , then shall the other sides be equal , each to each , and also the third of ...
... equal to two s of the other , each to each , and one side equal to one side , viz . , either the sides adj . to the equals in each , or the sides opp . to them , then shall the other sides be equal , each to each , and also the third of ...
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Euclid's Plane Geometry, Books III.-VI., Practically Applied; Or, Gradations ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
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Seite 7 - If two triangles have two sides of the one equal to two sides of the...
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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,
Seite 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