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 11.
Σελίδα 16
... arc and the smaller the minor conjugate arc . DEF . 5 . The conjugate angles formed at the centre of a circle by two radii are said to stand upon the coniugate arcs opposite them intercepted by the radii , the major angle upon the major ...
... arc and the smaller the minor conjugate arc . DEF . 5 . The conjugate angles formed at the centre of a circle by two radii are said to stand upon the coniugate arcs opposite them intercepted by the radii , the major angle upon the major ...
Σελίδα 20
... circle is the straight line joining any two points on the circumference . THEOR . 6. In the same circle , or in equal circles , equal arcs are subtended by equal chords ; and of two unequal minor arcs the greater is subtended by the ...
... circle is the straight line joining any two points on the circumference . THEOR . 6. In the same circle , or in equal circles , equal arcs are subtended by equal chords ; and of two unequal minor arcs the greater is subtended by the ...
Σελίδα 21
... minor arc DE be greater than the minor arc HK : then shall the chord DE be greater than the chord HK . Because the minor arc DE is greater than the minor arc HK : therefore the angle DAE of the triangle ADE is greater than the angle HBK ...
... minor arc DE be greater than the minor arc HK : then shall the chord DE be greater than the chord HK . Because the minor arc DE is greater than the minor arc HK : therefore the angle DAE of the triangle ADE is greater than the angle HBK ...
Σελίδα 22
... minor arc and the less major arc . Let DE , HK be chords of the equal circles DEF , HKL : then according as the chord DE is greater than , equal to , or less than , the chord HK , so shall the minor arc DE be greater than equal to , or ...
... minor arc and the less major arc . Let DE , HK be chords of the equal circles DEF , HKL : then according as the chord DE is greater than , equal to , or less than , the chord HK , so shall the minor arc DE be greater than equal to , or ...
Σελίδα 23
... arc ABC at B ; I. Prob . 4 . then shall the arc ABC be bisected at B. Because DE is the locus of points equidistant from A and C ; Loci , iii therefore the chord AB is equal to the chord BC ; therefore the arcs AB and BC , being both minor ...
... arc ABC at B ; I. Prob . 4 . then shall the arc ABC be bisected at B. Because DE is the locus of points equidistant from A and C ; Loci , iii therefore the chord AB is equal to the chord BC ; therefore the arcs AB and BC , being both minor ...
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...