The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
Inni boken
Resultat 1-5 av 5
Side 37
... standing on the same arc . Let BAC be at an angle at the circumference , BOC an angle at the centre standing on the same arc BEC : then shall the angle BAC be half the angle BOC . First let the centre O lie on AB , one of the arms of ...
... standing on the same arc . Let BAC be at an angle at the circumference , BOC an angle at the centre standing on the same arc BEC : then shall the angle BAC be half the angle BOC . First let the centre O lie on AB , one of the arms of ...
Side 38
... standing on the arc BEC . Next , let O lie within the angle BAC . E Join AO , and produce AO to meet the circumference at D. Then , as before , the angle BAO is half the angle BOD , and the angle OAC is half the angle DOC ; 38 THE ...
... standing on the arc BEC . Next , let O lie within the angle BAC . E Join AO , and produce AO to meet the circumference at D. Then , as before , the angle BAO is half the angle BOD , and the angle OAC is half the angle DOC ; 38 THE ...
Side 39
... standing on the arcs AC , BD . * Ex . 42. Two chords AB , CD , produced intersect at a point E without the circle . Shew that the angle AEC is half the difference of the angles at the centre standing on the arcs AC , BD . THEOR . 16 ...
... standing on the arcs AC , BD . * Ex . 42. Two chords AB , CD , produced intersect at a point E without the circle . Shew that the angle AEC is half the difference of the angles at the centre standing on the arcs AC , BD . THEOR . 16 ...
Side 40
... standing on the same arc , namely the arc BEC which is conjugate to the arc BADC , and therefore each is half of the angle BOC on the arc BEC : III . 15 . therefore the angle BAC is equal to the angle BDC . Ax . h . Q.E.D. COR . I. The ...
... standing on the same arc , namely the arc BEC which is conjugate to the arc BADC , and therefore each is half of the angle BOC on the arc BEC : III . 15 . therefore the angle BAC is equal to the angle BDC . Ax . h . Q.E.D. COR . I. The ...
Side 44
... standing on the arc BCD is half the angle BOD at the centre standing on the same arc BCD , III . 15 . and the angle BCD at the circumference standing on the arc BAD is half the angle BOD at the centre standing on the same arc BAD ...
... standing on the arc BCD is half the angle BOD at the centre standing on the same arc BCD , III . 15 . and the angle BCD at the circumference standing on the arc BAD is half the angle BOD at the centre standing on the same arc BAD ...
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...