The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Side 64
... externally at a point where they meet , if each lies outside the other ; to intersect if a part of each lies inside , and the remaining part outside the other ; and to touch internally at a point where they meet , if one of them lies ...
... externally at a point where they meet , if each lies outside the other ; to intersect if a part of each lies inside , and the remaining part outside the other ; and to touch internally at a point where they meet , if one of them lies ...
Side 66
... externally or internally ; and the distance between their centres is in the former case equal to the sum , and in the latter to the difference , of the radii . Let the circumferences of two circles whose centres are A and B meet at the ...
... externally or internally ; and the distance between their centres is in the former case equal to the sum , and in the latter to the difference , of the radii . Let the circumferences of two circles whose centres are A and B meet at the ...
Side 67
... externally . III . Def . 14 . I. 13 . In fig . 2 AD is less than the sum of AB and BD , and BD is equal to BC ; therefore AD is less than AC ; therefore D is within the circle whose centre is A ; III . I , Cor . therefore the circle ...
... externally . III . Def . 14 . I. 13 . In fig . 2 AD is less than the sum of AB and BD , and BD is equal to BC ; therefore AD is less than AC ; therefore D is within the circle whose centre is A ; III . I , Cor . therefore the circle ...
Side 68
... externally , ( 3 ) intersect , ( 4 ) touch each other internally , ( 5 ) lie one inside the other . Shew that these statements follow from the preceding statements by the Rule of Conversion , and give also a direct geometrical proof of ...
... externally , ( 3 ) intersect , ( 4 ) touch each other internally , ( 5 ) lie one inside the other . Shew that these statements follow from the preceding statements by the Rule of Conversion , and give also a direct geometrical proof of ...
Side 70
... externally , AB is equal to the sum of their radii , and B lies on the circumference of one of the circles used in the construction and outside the other , and three common tangents can be drawn ; if the circles intersect , AB is less ...
... externally , AB is equal to the sum of their radii , and B lies on the circumference of one of the circles used in the construction and outside the other , and three common tangents can be drawn ; if the circles intersect , AB is less ...
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 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
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...