## Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations in Euclid, part ii., with illustr. [&c.] by H. Green |

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Euclid's Plane Geometry, Books III.-VI., Practically Applied; Or, Gradations ... Euclides Sin vista previa disponible - 2016 |

### Términos y frases comunes

ABCD Antecs base bisected centre chord circumference circumscribed Cone contained decagon desc diam diameter divided draw drawn equiangular equims equimultiples Euclid extreme fourth Geometry given circle given line given st greater hypotenuse inscribed isosc join less multiple parallel parallelogram pentagon perp Plane Geometry polygon Prop propl proportional proposition 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

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Página 7 - If two triangles have two sides of the one equal to two sides of the...

Página 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...

Página 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.

Página 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.

Página 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.

Página 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.

Página 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...

Página 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.

Página 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,

Página 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