The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Σελίδα 37
... angle formed by any two chords drawn from a point on the circumference of a ... BAC be at an angle at the circumference , BOC an angle at the centre ... ANGLES IN SEGMENTS . 37 Section IV Angles in Segments.
... angle formed by any two chords drawn from a point on the circumference of a ... BAC be at an angle at the circumference , BOC an angle at the centre ... ANGLES IN SEGMENTS . 37 Section IV Angles in Segments.
Σελίδα 38
... angles OAC , OCA ; therefore the angle BAC is half the angle BOC , 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 ...
... angles OAC , OCA ; therefore the angle BAC is half the angle BOC , 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 ...
Σελίδα 39
Association for the Improvement of Geometrical Teaching. and the angle OAC is half the angle DOC ; therefore the whole angle BAC is half the whole angle BOC standing on the arc BEC . Again , let O lie without the angle BAC : B As before ...
Association for the Improvement of Geometrical Teaching. and the angle OAC is half the angle DOC ; therefore the whole angle BAC is half the whole angle BOC standing on the arc BEC . Again , let O lie without the angle BAC : B As before ...
Σελίδα 40
Association for the Improvement of Geometrical Teaching. Let BAC , BDC be angles in the same segment BADC ; E E then shall the angle BAC be equal to the angle BDC . Take O the centre of the circle ; join OB , OC . Then the angles BAC , BDC ...
Association for the Improvement of Geometrical Teaching. Let BAC , BDC be angles in the same segment BADC ; E E then shall the angle BAC be equal to the angle BDC . Take O the centre of the circle ; join OB , OC . Then the angles BAC , BDC ...
Σελίδα 41
... BAC . COR . 2. The locus of a point on one side of a given finite straight line at which that line subtends a constant angle is an arc of which that line is the chord . * Ex ... BAC be an angle in the segment BAC of ANGLES IN SEGMENTS . 41.
... BAC . COR . 2. The locus of a point on one side of a given finite straight line at which that line subtends a constant angle is an arc of which that line is the chord . * Ex ... BAC be an angle in the segment BAC of ANGLES IN SEGMENTS . 41.
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
Σελίδα 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.
Σελίδα 171 - ... are to one another in the duplicate ratio of their homologous sides.
Σελίδα 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.
Σελίδα 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...
Σελίδα 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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.
Σελίδα 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...