Elements of Geometry: With NotesJ. Souter, 1827 - 208 σελίδες |
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Σελίδα 2
... vertex . Thus the angle contained by the straight lines AB , BC , is designated as the angle B. When , however , two or more angles have the same vertex , then , in order to denote any one in particular , it becomes necessary to specify ...
... vertex . Thus the angle contained by the straight lines AB , BC , is designated as the angle B. When , however , two or more angles have the same vertex , then , in order to denote any one in particular , it becomes necessary to specify ...
Σελίδα 4
... vertices of two opposite angles of a quadrilateral , is called a diagonal . Thus the line AC joining the vertices of the opposite angles DAB , DCB of the quad- rilateral ABCD , is a diagonal . A D B 25. Plane figures are equal when , by ...
... vertices of two opposite angles of a quadrilateral , is called a diagonal . Thus the line AC joining the vertices of the opposite angles DAB , DCB of the quad- rilateral ABCD , is a diagonal . A D B 25. Plane figures are equal when , by ...
Σελίδα 8
... vertex , the adjacent angle formed will be right . Cor . 2. Therefore the sides of a right angle are mutually perpendicular . E Cor . 3. The sum of all the angles formed by straight lines drawn on the same side of another straight line ...
... vertex , the adjacent angle formed will be right . Cor . 2. Therefore the sides of a right angle are mutually perpendicular . E Cor . 3. The sum of all the angles formed by straight lines drawn on the same side of another straight line ...
Σελίδα 15
... vertices which the parallel side lies on , or else each upon the opposite side of that line . Let the sides of the angles BAC , DEF , be parallel each to each , and let AB lie upon the same side of AE as the parallel side ED , and let ...
... vertices which the parallel side lies on , or else each upon the opposite side of that line . Let the sides of the angles BAC , DEF , be parallel each to each , and let AB lie upon the same side of AE as the parallel side ED , and let ...
Σελίδα 16
... vertex , the exterior angle will be double of either angle at the base , and if the base be produced , the ex ... vertices of the several angles , 16 ELEMENTS OF GEOMETRY .
... vertex , the exterior angle will be double of either angle at the base , and if the base be produced , the ex ... vertices of the several angles , 16 ELEMENTS OF GEOMETRY .
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 136 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 179 - FC, and the triangle ABD to the triangle FBC. Now the parallelogram BL is double...
Σελίδα 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.