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 9.
Σελίδα 77
... polygon formed by the chords of these arcs is regular ; and the circumscribed polygon formed by tangents drawn at all the points of division is also regular . Let the whole circumference of the circle ABC be divided into any number ...
... polygon formed by the chords of these arcs is regular ; and the circumscribed polygon formed by tangents drawn at all the points of division is also regular . Let the whole circumference of the circle ABC be divided into any number ...
Σελίδα 78
... polygon ABCD • be regular . · • are all equal , Hyp . are all equal ; III . 6 . is equilateral . ... Again , each angle of the polygon ABCD ... stands upon an arc which is less than the whole circumference by two of the arcs AB , BC ...
... polygon ABCD • be regular . · • are all equal , Hyp . are all equal ; III . 6 . is equilateral . ... Again , each angle of the polygon ABCD ... stands upon an arc which is less than the whole circumference by two of the arcs AB , BC ...
Σελίδα 79
... polygon is equal to the next succeeding angle ; therefore the polygon is equiangular . Hence the polygon is regular . I. Def . 23 . Q.E.D. Ex . 116. Any equilateral figure inscribed in a circle is also equiangular . Ex . 117 . In any ...
... polygon is equal to the next succeeding angle ; therefore the polygon is equiangular . Hence the polygon is regular . I. Def . 23 . Q.E.D. Ex . 116. Any equilateral figure inscribed in a circle is also equiangular . Ex . 117 . In any ...
Σελίδα 80
... polygon at A , and the angle at A is equal to the angle at C ; therefore the angle OCB is half the angle at C , that is , OC bisects the angle at C. Нур . Hyp . I. 5 . Hyp . Hyp . In like manner OD .. bisects the other angles of the polygon ...
... polygon at A , and the angle at A is equal to the angle at C ; therefore the angle OCB is half the angle at C , that is , OC bisects the angle at C. Нур . Hyp . I. 5 . Hyp . Hyp . In like manner OD .. bisects the other angles of the polygon ...
Σελίδα 81
... polygon : it is required to circumscribe a circle about , and to inscribe a circle in , the polygon ABCD ... K Bisect two adjacent angles A , B of the polygon , and let the bisectors meet at O , draw OK perpendicular to AB , describe ...
... polygon : it is required to circumscribe a circle about , and to inscribe a circle in , the polygon ABCD ... K Bisect two adjacent angles A , B of the polygon , and let the bisectors meet at O , draw OK perpendicular to AB , describe ...
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...