The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Side 13
... Prove that if a curve is symmetrical with respect to every axis through a given point , it is a circle whose centre is that point . THEOR . 3 . Circles of equal radii are identically equal . Let DEF , HKL be two circles of equal radii ...
... Prove that if a curve is symmetrical with respect to every axis through a given point , it is a circle whose centre is that point . THEOR . 3 . Circles of equal radii are identically equal . Let DEF , HKL be two circles of equal radii ...
Side 15
... prove that the vertices of equilateral triangles described upon them as bases will be on two fixed circles . Enunciate and prove a similar theorem as regards squares . 14. A point is taken outside a fixed circle at a dis- tance from the ...
... prove that the vertices of equilateral triangles described upon them as bases will be on two fixed circles . Enunciate and prove a similar theorem as regards squares . 14. A point is taken outside a fixed circle at a dis- tance from the ...
Side 26
... proved geometrically , the other two follow by the Rule of Identity . * Ex . 26. The locus of the centres of all circles that pass through two given points is the straight line that bisects at right angles the line joining those points ...
... proved geometrically , the other two follow by the Rule of Identity . * Ex . 26. The locus of the centres of all circles that pass through two given points is the straight line that bisects at right angles the line joining those points ...
Side 30
... Prove that two circles cannot have a common arc . THEOR . 13. In the same circle , or in equal circles , equal chords are equally distant from the centre ; and of two unequal chords the greater is nearer to the centre than the less . In ...
... Prove that two circles cannot have a common arc . THEOR . 13. In the same circle , or in equal circles , equal chords are equally distant from the centre ; and of two unequal chords the greater is nearer to the centre than the less . In ...
Side 35
... Prove that the diameter is the greatest chord in a circle directly by I. 13 . * Ex . 29. Prove Theors . 13 and 14 directly by II . 9 . EXERCISES . 30. If the straight lines which bisect at right angles the sides of a rectilineal figure ...
... Prove that the diameter is the greatest chord in a circle directly by I. 13 . * Ex . 29. Prove Theors . 13 and 14 directly by II . 9 . EXERCISES . 30. If the straight lines which bisect at right angles the sides of a rectilineal figure ...
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...