The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Αποτελέσματα 1 - 5 από τα 31.
Σελίδα 41
... triangle DEC is greater than the interior opposite angle DEC ; I. 9 . that is , the angle BDC is greater than the angle BEC which is in the segment ABC . In like manner it may be shown that if D is a point outside the segment ABC and on ...
... triangle DEC is greater than the interior opposite angle DEC ; I. 9 . that is , the angle BDC is greater than the angle BEC which is in the segment ABC . In like manner it may be shown that if D is a point outside the segment ABC and on ...
Σελίδα 45
... angle . COR . 2 . If the opposite angles of a quadrilateral are supplementary a circle can be described about the quadri ... triangle ABC , perpendiculars DE , DF are drawn to the sides . Prove that B , E ANGLES IN SEGMENTS . 45 16 20.
... angle . COR . 2 . If the opposite angles of a quadrilateral are supplementary a circle can be described about the quadri ... triangle ABC , perpendiculars DE , DF are drawn to the sides . Prove that B , E ANGLES IN SEGMENTS . 45 16 20.
Σελίδα 47
... triangles described on the sides of any triangle and external to the triangle meet in a point . 65. Upon the sides of the triangle ABC the equilateral triangles A'BC , B'CA , and C'AB are constructed , the vertices A and A ' being on ...
... triangles described on the sides of any triangle and external to the triangle meet in a point . 65. Upon the sides of the triangle ABC the equilateral triangles A'BC , B'CA , and C'AB are constructed , the vertices A and A ' being on ...
Σελίδα 48
... triangles which have a given base and vertical angle , the greatest is that in which the two sides are equal . 72. Two circles intersect at the points A and B. In the circumference of one of the circles ABC any point P is taken , and ...
... triangles which have a given base and vertical angle , the greatest is that in which the two sides are equal . 72. Two circles intersect at the points A and B. In the circumference of one of the circles ABC any point P is taken , and ...
Σελίδα 56
Association for the Improvement of Geometrical Teaching. circle ABC , as DE , is not a tangent to ABC , since the ... triangle . Shew that the hypotenuse together with the diameter is equal to the sum of the other two sides . Ex . 81. If ...
Association for the Improvement of Geometrical Teaching. circle ABC , as DE , is not a tangent to ABC , since the ... triangle . Shew that the hypotenuse together with the diameter is equal to the sum of the other two sides . Ex . 81. If ...
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...