Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith1876 - 349 páginas |
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Página 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 ...
Página 129
Euclides, James Hamblin SMITH. PROPOSITION VI . THEOREM . If one circle touch another internally , they cannot have the same centre . A D C E Let ADE touch ABC internally , and let A be a point of contact . Then some point E in the Oce ...
Euclides, James Hamblin SMITH. PROPOSITION VI . THEOREM . If one circle touch another internally , they cannot have the same centre . A D C E Let ADE touch ABC internally , and let A be a point of contact . Then some point E in the Oce ...
Página 135
... that O will coincide with the middle point of BC . Ex . 2. If BAC be an obtuse angle , shew that O will fall on the side of BC remote from A. PROPOSITION XI . THEOREM . If one circle touch another Book III . ] 135 PROPOSITION B.
... that O will coincide with the middle point of BC . Ex . 2. If BAC be an obtuse angle , shew that O will fall on the side of BC remote from A. PROPOSITION XI . THEOREM . If one circle touch another Book III . ] 135 PROPOSITION B.
Página 136
... touch the ABC internally , and let A be a pt . of contact . Find O 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 ...
... touch the ABC internally , and let A be a pt . of contact . Find O 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 ...
Página 137
... touch ADE externally at the pt . A. Let O be the centre of O ABC . Join OA , and produce it to E. Then must the centre of ADE lie in AE . For if not , let P be the centre of ADE . Join OP meeting the Os in B , D ; and join AP . Then OB ...
... touch ADE externally at the pt . A. Let O be the centre of O ABC . Join OA , and produce it to E. Then must the centre of ADE lie in AE . For if not , let P be the centre of ADE . Join OP meeting the Os in B , D ; and join AP . Then OB ...
Otras ediciones - Ver todas
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Sin vista previa disponible - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Sin vista previa disponible - 2018 |
Términos y frases comunes
ABCD angles equal angular points base BC BC=EF bisecting the angle centre chord circumference coincide diagonals diameter divided equal angles equal circles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater than nD Hence inscribed isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius rectangle contained reflex angle required to describe rhombus right angles segment semicircle shew shewn straight line joining subtended sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Pasajes populares
Página 51 - 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.
Página 38 - 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. either the sides adjacent to the equal...
Página 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.
Página 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon...
Página 50 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Página 104 - 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.
Página 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 89 - 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.
Página 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.
Página 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.