The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Σελίδα 7
... Magnitudes only . Section I. Of Ratio and Proportion Section II Fundamental Geometrical Propositions Definitions 109 117 · 125 PAGE PART II . Magnitudes without respect to Commensurability .
... Magnitudes only . Section I. Of Ratio and Proportion Section II Fundamental Geometrical Propositions Definitions 109 117 · 125 PAGE PART II . Magnitudes without respect to Commensurability .
Σελίδα 8
Association for the Improvement of Geometrical Teaching. PAGE PART II . Magnitudes without respect to Commensurability . Section I. Of Ratio and Proportion 127 Section II . Fundamental Geometrical Propositions 144 Definitions 149 BOOK V ...
Association for the Improvement of Geometrical Teaching. PAGE PART II . Magnitudes without respect to Commensurability . Section I. Of Ratio and Proportion 127 Section II . Fundamental Geometrical Propositions 144 Definitions 149 BOOK V ...
Σελίδα 59
... magnitude whatever be the position of G in the arc ACB . Let G move up to , and ultimately coincide with , A : then the secant HK ultimately becomes the tangent at A , III . 16 . III . Def . 13 , Aliter . and the angle BGK ultimately ...
... magnitude whatever be the position of G in the arc ACB . Let G move up to , and ultimately coincide with , A : then the secant HK ultimately becomes the tangent at A , III . 16 . III . Def . 13 , Aliter . and the angle BGK ultimately ...
Σελίδα 100
... magnitude of the angles of the figure ? 191. The circumference of one circle passes through the centre of another circle . If from any point in the circumfer- ence of the former circle two straight lines be drawn to touch the latter ...
... magnitude of the angles of the figure ? 191. The circumference of one circle passes through the centre of another circle . If from any point in the circumfer- ence of the former circle two straight lines be drawn to touch the latter ...
Σελίδα 105
... magnitudes in general , and not merely geometrical magnitudes — such as lines , angles , areas , etc. Many of the propositions are familiar , under somewhat different forms , to those who have studied Arithmetic and Elementary Algebra ...
... magnitudes in general , and not merely geometrical magnitudes — such as lines , angles , areas , etc. Many of the propositions are familiar , under somewhat different forms , to those who have studied Arithmetic and Elementary Algebra ...
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...