Elements of Geometry: With NotesJ. Souter, 1827 - 208 σελίδες |
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Σελίδα 13
... exterior angles be equal , the two lines will be parallel . Cor . 3. Hence , likewise , if the two exterior angles on the same side ( as ABE , DCG ) be together equal to two right angles , the two lines will be parallel . Cor . 4. Also ...
... exterior angles be equal , the two lines will be parallel . Cor . 3. Hence , likewise , if the two exterior angles on the same side ( as ABE , DCG ) be together equal to two right angles , the two lines will be parallel . Cor . 4. Also ...
Σελίδα 15
... exterior angle equal to the interior opposite one , on the same side of the cutting line . Cor . 2. The alternate exterior angles ( ABE , DCH ) are also equal . Cor . 3. The two exterior angles also ( ABE , DCG ) on the same side are ...
... exterior angle equal to the interior opposite one , on the same side of the cutting line . Cor . 2. The alternate exterior angles ( ABE , DCH ) are also equal . Cor . 3. The two exterior angles also ( ABE , DCG ) on the same side are ...
Σελίδα 16
... exterior angle will be equal to both the interior opposite angles . Let one ofthe sides as BC of the triangle ABC be ... exterior angle ECD ( Prop . XIV . Cor . 1. ) ; therefore the , sum of the angles A and B is equal to the sum of ACE ...
... exterior angle will be equal to both the interior opposite angles . Let one ofthe sides as BC of the triangle ABC be ... exterior angle ECD ( Prop . XIV . Cor . 1. ) ; therefore the , sum of the angles A and B is equal to the sum of ACE ...
Σελίδα 17
... exterior angles , formed by pro- ducing each side , amount to four right angles . Let each side of the polygon in the margin be produced , the exterior angles shall amount to four right angles . For each exterior angle , together with ...
... exterior angles , formed by pro- ducing each side , amount to four right angles . Let each side of the polygon in the margin be produced , the exterior angles shall amount to four right angles . For each exterior angle , together with ...
Σελίδα 18
... exterior angles will not be formed , but interior ones as shown in the above dia- gram . PROPOSITION XIX . THEOREM . In any triangle the greater angle is opposite to the longer side . Let the side AC of the triangle ABC be longer than ...
... exterior angles will not be formed , but interior ones as shown in the above dia- gram . PROPOSITION XIX . THEOREM . In any triangle the greater angle is opposite to the longer side . Let the side AC of the triangle ABC be longer than ...
Άλλες εκδόσεις - Προβολή όλων
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.