Elements of Geometry: With NotesJ. Souter, 1827 - 208 sider |
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Side 39
... radii and the intercepted arc . The space CBDC is a sector of the circle . 10. A tangent is a line which touches the circumference , that is , it has but one point in common with it , which point is called the point of contact . 11. One ...
... radii and the intercepted arc . The space CBDC is a sector of the circle . 10. A tangent is a line which touches the circumference , that is , it has but one point in common with it , which point is called the point of contact . 11. One ...
Side 48
... radii , the circumferences touch exter- nally . Cor . 3. But if the distance be equal to the difference of the radii , one touches the other internally , for in both cases the cir- cumferences pass through the same point in the line ...
... radii , the circumferences touch exter- nally . Cor . 3. But if the distance be equal to the difference of the radii , one touches the other internally , for in both cases the cir- cumferences pass through the same point in the line ...
Side 49
... radii ; for CD is less than the sum of CA , DA ( Prop . XXI . B. I. ) ; and , consequently , that , if the distance of the centres of two circles be greater than the sum of their radii , the circumferences will neither touch ( Prop ...
... radii ; for CD is less than the sum of CA , DA ( Prop . XXI . B. I. ) ; and , consequently , that , if the distance of the centres of two circles be greater than the sum of their radii , the circumferences will neither touch ( Prop ...
Side 117
... radii of these circles , and in each case the sur- faces of the polygons are as the squares of the radii . First , let the similar polygons in the margin admit of in- scribed circles , whose centres are O , o - their perimeters will be ...
... radii of these circles , and in each case the sur- faces of the polygons are as the squares of the radii . First , let the similar polygons in the margin admit of in- scribed circles , whose centres are O , o - their perimeters will be ...
Side 118
... radii of the cir- cumscribed circles ; and it moreover follows , as above , that the surfaces are as the squares of the radii . Cor . About , or within a circle , a polygon may be described similar to any inscribed or circumscribed ...
... radii of the cir- cumscribed circles ; and it moreover follows , as above , that the surfaces are as the squares of the radii . Cor . About , or within a circle , a polygon may be described similar to any inscribed or circumscribed ...
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Vanlige uttrykk og setninger
ABCD adjacent angles altitude angle ABC angle ACB angle BAC antecedent base centre chord circ circle circumference circumscribed polygon coincide consequently Prop construction Converse of Prop corollary demonstration described diagonals diameter divided draw enveloping line equal angles equal Prop equimultiples equivalent Euclid exterior angle follows four right angles geometry gonal greater half hence homologous sides hypothenuse hypothesis included angle inscribed angle inscribed polygon intersect isosceles triangle join Legendre less line drawn lines be drawn magnitudes meet multiple number of sides obtuse opposite angles parallel perimeter perpendicular PROBLEM proportion PROPOSITION XII quadrilateral radii rectangle rectangle contained regular polygon respectively equal rhomboid right angled triangle Scholium shorter side BC similar polygons similar triangles submultiple subtended surface tangent THEOREM three angles tiple triangle ABC vertex VIII
Populære avsnitt
Side 159 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. 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 the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Side 24 - 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. Let...
Side 80 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Side 179 - FBC ; and because the two sides AB, BD are equal to the two FB, BC, each to each, and the angle DBA equal to the angle FBC ; therefore the base AD is equal to the base FC, and the triangle ABD to the triangle FBC.
Side 136 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 179 - BK, it is demonstrated that the parallelogram CL is equal to the square HC. Therefore the whole square BDEC is equal to the two squares GB, HC ; and the square BDEC is described upon the straight line BC, and the squares GB, HC upon BA, AC.
Side 99 - And since a radius drawn to the point of contact is perpendicular to the tangent, it follows that the angle included by two tangents, drawn from the same point, is bisected by a line drawn from the centre of the circle to that point ; for this line forms the hypotenuse common to two equal right angled triangles. PROP. XXXVII. THEOR. If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle...
Side 29 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Side 179 - FC, and the triangle ABD to the triangle FBC. Now the parallelogram BL is double...
Side 165 - This formula already proves, that if two angles of one triangle are equal to two angles of another, the third angle of the former must also be equal to the third of the latter ; and this granted, it is easy to arrive at the theorem we have in view.