Elements of Geometry: With NotesJ. Souter, 1827 - 208 σελίδες |
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Αποτελέσματα 1 - 5 από τα 32.
Σελίδα 10
... included angle in one triangle be equal to two sides , and the included angle in another triangle , those triangles shall be equal . Let the triangles ABC , DEF , have the sides AB , AC , and the included angle A in the one equal to the ...
... included angle in one triangle be equal to two sides , and the included angle in another triangle , those triangles shall be equal . Let the triangles ABC , DEF , have the sides AB , AC , and the included angle A in the one equal to the ...
Σελίδα 11
... included angle in the one are equal to the two sides AC , AD , and the in- cluded angle in the other ; hence the ... included angle , are equal to BC , CA , and the included angle , A 11 BOOK I.
... included angle in the one are equal to the two sides AC , AD , and the in- cluded angle in the other ; hence the ... included angle , are equal to BC , CA , and the included angle , A 11 BOOK I.
Σελίδα 12
... included angle B , are respectively equal to DE , EF , and the included angle E , the angle BCG must be equal to the angle F ( Prop . VII . ) ; but by hypothesis , the angle F is equal to the angle ACB ; hence , then the angle GCB is ...
... included angle B , are respectively equal to DE , EF , and the included angle E , the angle BCG must be equal to the angle F ( Prop . VII . ) ; but by hypothesis , the angle F is equal to the angle ACB ; hence , then the angle GCB is ...
Σελίδα 13
... included angle in the one equal re- spectively to the two sides KM , MC , and the included angle in the other ; hence the angle IBM is equal to the angle KCM ( Prop . VIII . ) ; but by hypothesis , the angle IBM is equal to the angle ...
... included angle in the one equal re- spectively to the two sides KM , MC , and the included angle in the other ; hence the angle IBM is equal to the angle KCM ( Prop . VIII . ) ; but by hypothesis , the angle IBM is equal to the angle ...
Σελίδα 20
... included angle are equal to EF , FP , and the included angle PD is equal to PE ( Prop . VIII . ) ; hence lines drawn from Pintercepting equal distances from the perpendicular are equal . Lastly , because the triangle PDE is isosceles ...
... included angle are equal to EF , FP , and the included angle PD is equal to PE ( Prop . VIII . ) ; hence lines drawn from Pintercepting equal distances from the perpendicular are equal . Lastly , because the triangle PDE is isosceles ...
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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.