Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |
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Resultat 1-5 av 34
Side 128
... touch each other , which meet but do not cut each other . One circle is said to touch another internally , when one point of the circumference of the former lies on , and no point without , the circumference of the other . Hence for ...
... touch each other , which meet but do not cut each other . One circle is said to touch another internally , when one point of the circumference of the former lies on , and no point without , the circumference of the other . Hence for ...
Side 129
Euclides, James Hamblin Smith. PROPOSITION VI . THEOREM . If one circle touch another internally , they cannot have the same centre . B E Let ADE touch o ABC internally , and let A be a point of contact . Then some point E in the Oce ADE ...
Euclides, James Hamblin Smith. PROPOSITION VI . THEOREM . If one circle touch another internally , they cannot have the same centre . B E Let ADE touch o ABC internally , and let A be a point of contact . Then some point E in the Oce ADE ...
Side 135
... a OA , this will be the required . Q. E. F. Ex . If BAC be a right angle , show that O will coincide with the middle point of BC . PROPOSITION XI . THEOREM . If one circle touch another Book III . ] 135 PROPOSITION B.
... a OA , this will be the required . Q. E. F. Ex . If BAC be a right angle , show that O will coincide with the middle point of BC . PROPOSITION XI . THEOREM . If one circle touch another Book III . ] 135 PROPOSITION B.
Side 136
... touch the ABC internally , and let A be a pt . of contact . Find the centre of ○ ABC , and join OA . Then must the centre of ADE lie in the radius OA . For if not , let P be the centre of ADE . Join OP , and produce it to meet the Oces ...
... touch the ABC internally , and let A be a pt . of contact . Find the centre of ○ ABC , and join OA . Then must the centre of ADE lie in the radius OA . For if not , let P be the centre of ADE . Join OP , and produce it to meet the Oces ...
Side 137
... touch ADE externally at the pt . A. Let O be the centre of ABC . Join OA , and produce it to E. Then must the centre of For if not , let P be the centre of ADE lie in AE . ADE . E Join OP meeting the © s in B , D ; and join AP . Then OB ...
... touch ADE externally at the pt . A. Let O be the centre of ABC . Join OA , and produce it to E. Then must the centre of For if not , let P be the centre of ADE lie in AE . ADE . E Join OP meeting the © s in B , D ; and join AP . Then OB ...
Vanlige uttrykk og setninger
AB=DE ABCD AC=DF angle equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater Hence hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram pentagon perpendicular polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained rectilinear figure reflex angle rhombus right angles segment Shew shewn square straight lines drawn sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Populære avsnitt
Side 42 - 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 53 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 17 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Side 106 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Side 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 188 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 78 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Side 5 - 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.