Elements of Geometry: With NotesJ. Souter, 1827 - 208 σελίδες |
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Σελίδα 39
... 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 circle touches another when their circumferences have one point in common , and ...
... 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 circle touches another when their circumferences have one point in common , and ...
Σελίδα 45
... tangent to the circle , and , conversely , a tangent to a circle is perpendicular to the diameter drawn from the point of contact . Let ABD be perpendicular to the radius CB , it shall touch the circle in the point B .. For to show that ...
... tangent to the circle , and , conversely , a tangent to a circle is perpendicular to the diameter drawn from the point of contact . Let ABD be perpendicular to the radius CB , it shall touch the circle in the point B .. For to show that ...
Σελίδα 46
... tangents are both perpen- dicular to the same diameter ( Prop . XIV . Cor . 5. B. Î . ) , and have their points of contact at its extremities . Scholium . This proposition shows the possibility of the existence of a tangent to a circle ...
... tangents are both perpen- dicular to the same diameter ( Prop . XIV . Cor . 5. B. Î . ) , and have their points of contact at its extremities . Scholium . This proposition shows the possibility of the existence of a tangent to a circle ...
Σελίδα 47
... tangent AB ( Prop . IX . ) ; therefore AB , GH are parallel . If both lines cut the circle , as GH , JK , and intercept equal arcs GJ , HK , let the diameter FE bisect one of the chords , as GH : it will also bisect the arc GEH ( Prop ...
... tangent AB ( Prop . IX . ) ; therefore AB , GH are parallel . If both lines cut the circle , as GH , JK , and intercept equal arcs GJ , HK , let the diameter FE bisect one of the chords , as GH : it will also bisect the arc GEH ( Prop ...
Σελίδα 48
... tangent to either , it would be perpendicular either to DA , or CA , which it is not ; let it then cut the circumference , whose centre is C , in the point E , then the chord AE is bisected in B ( Prop . V. ) ; let it cut the other ...
... tangent to either , it would be perpendicular either to DA , or CA , which it is not ; let it then cut the circumference , whose centre is C , in the point E , then the chord AE is bisected in B ( Prop . V. ) ; let it cut the other ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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 equal angles equal Prop equal to AC equimultiples equivalent Euclid exterior angle follows four right angles geometry given straight line 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 side BC similar polygons similar triangles submultiple subtended surface tangent THEOREM three angles tiple triangle ABC vertex VIII
Δημοφιλή αποσπάσματα
Σελίδα 165 - ... 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.
Σελίδα 172 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 30 - 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...
Σελίδα 185 - 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 (i.
Σελίδα 86 - 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...
Σελίδα 142 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 205 - Let AMB be the enveloped line; then will it be less than the line APDB which envelopes it. We have already said that by the term convex line we understand a line, polygonal, or curve, or partly curve and . partly polygonal, such that a straight line cannot cut it in more than two points.
Σελίδα 185 - 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.
Σελίδα 105 - 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...
Σελίδα 35 - 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.