The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Side 9
... radius of a circle is a straight line drawn from the centre to the circumference . DEF . 3. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . THEOR . I. The distance of ...
... radius of a circle is a straight line drawn from the centre to the circumference . DEF . 3. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . THEOR . I. The distance of ...
Side 10
... radius , according as P is within , on , or without the circumference . The straight line passing through O and P ... radius . If P is between Q and Q ' , P is within the circumference , and OP is less than OQ , that is , less than the ...
... radius , according as P is within , on , or without the circumference . The straight line passing through O and P ... radius . If P is between Q and Q ' , P is within the circumference , and OP is less than OQ , that is , less than the ...
Side 12
... radius on the other side of AOB , and making with OB the angle BOQ equal to BOP . I. Prob . 5 . Then , if APB be turned about AB till it lies on the same side of AB with AQB , and in the same plane with it , OP will fall along OQ ...
... radius on the other side of AOB , and making with OB the angle BOQ equal to BOP . I. Prob . 5 . Then , if APB be turned about AB till it lies on the same side of AB with AQB , and in the same plane with it , OP will fall along OQ ...
Side 14
... radius of the circle DEF , and therefore equal to the radius of HKL . III . 1 , Cor . In like manner , any point on the circumference of HKL will fall on the circumference of DEF . Hence the two circumferences coincide , and therefore ...
... radius of the circle DEF , and therefore equal to the radius of HKL . III . 1 , Cor . In like manner , any point on the circumference of HKL will fall on the circumference of DEF . Hence the two circumferences coincide , and therefore ...
Side 15
... radius . Shew that a straight line may be drawn through the point to cut the circle in such a way that the part of the line between the point and the circle is equal to the part intercepted by the circle . 15. If two straight lines be ...
... radius . Shew that a straight line may be drawn through the point to cut the circle in such a way that the part of the line between the point and the circle is equal to the part intercepted by the circle . 15. If two straight lines be ...
Vanlige uttrykk og setninger
ABCD angle ABC angle BAC angle DAE angle DEF angle HBK angular points antecedent base chord HK circle ABC circle whose centre circles touch circumscribed circle decagon diagonal diameter divided internally draw duplicate ratio equal angles equiangular equimultiples externally given circle given point given ratio given straight line greater half the angle Hence homologous sides inscribed circle isosceles triangle less Let ABC line joining mean proportional meet the circumference middle point minor arc HK multiple nine-points circle orthocentre parallel parallelogram perpendicular PLANE GEOMETRY point of contact polygon Prob Prove Q.E.D. THEOR quadrilateral radii radius ratio compounded ratios are equal rectangle BD rectangle contained rectilineal figure right angles sector segment BAC semicircle Shew side BC square straight line drawn tangent triangle ABC triangle DEF vertical angle
Populære avsnitt
Side 167 - 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.
Side 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
Side 30 - In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Side 171 - ... are to one another in the duplicate ratio of their homologous sides.
Side 150 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Side 115 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let...
Side 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 96 - ... 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.
Side 150 - When there are any number of magnitudes of the same kind, the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second, and of the ratio whi.ch the second has to the third, and of the ratio which the third has to the fourth, and so on unto the last magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first...