The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Resultat 1-5 av 63
Side 9
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another . This point is called the centre of the circle . DEF . 2. A radius of a circle is a straight ...
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another . This point is called the centre of the circle . DEF . 2. A radius of a circle is a straight ...
Side 10
... circumference . The straight line passing through O and P will meet the cir- cumference in two points Q , Q ' , and ... circumference , and OP is less than OQ , that is , less than the radius . If P coincide with Q or Q ' , P is on the ...
... circumference . The straight line passing through O and P will meet the cir- cumference in two points Q , Q ' , and ... circumference , and OP is less than OQ , that is , less than the radius . If P coincide with Q or Q ' , P is on the ...
Side 14
... circumference of DEF will fall on the circumference of HKL , since its distance from the centre of HKL is a radius of the circle DEF , and therefore equal to the radius of HKL . III . 1 , Cor . In like manner , any point on the ...
... circumference of DEF will fall on the circumference of HKL , since its distance from the centre of HKL is a radius of the circle DEF , and therefore equal to the radius of HKL . III . 1 , Cor . In like manner , any point on the ...
Side 15
... circumference . 12. The lines joining any fixed point to any number of points on the circumference of a given circle are bisected . Shew that the middle points all lie on the circumference of another fixed circle . 13 . If lines are ...
... circumference . 12. The lines joining any fixed point to any number of points on the circumference of a given circle are bisected . Shew that the middle points all lie on the circumference of another fixed circle . 13 . If lines are ...
Side 16
... circumference . Two arcs , which together make the whole circumference , are said to be conjugate . The greater of the two is called the major conjugate arc and the smaller the minor conjugate arc . DEF . 5 . The conjugate angles formed ...
... circumference . Two arcs , which together make the whole circumference , are said to be conjugate . The greater of the two is called the major conjugate arc and the smaller the minor conjugate arc . DEF . 5 . The conjugate angles formed ...
Vanlige uttrykk og setninger
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 hypotenuse 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 point of contact polygon Prob Prove Q.E.D. THEOR quadrilateral radii radius ratio compounded ratios are equal rectangle AC rectangle contained rectilineal figure rhombus right angles sector segment BAC semicircle Shew side BC square straight line drawn tangent triangle ABC triangle DEF vertical angle
Populære avsnitt
Side 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.
Side 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.
Side 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
Side 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.
Side 171 - ... are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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...
Side 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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.
Side 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...