Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 44.
Σελίδα 24
... angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF ... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz ...
... angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF ... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz ...
Σελίδα 25
... angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles are equal , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG ...
... angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles are equal , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG ...
Σελίδα 30
... angle CBE is equal to the two angles CBA , АВЕ together ; add the angle EBD to each of these equals , and the two ... remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight ...
... angle CBE is equal to the two angles CBA , АВЕ together ; add the angle EBD to each of these equals , and the two ... remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight ...
Σελίδα 31
... angle AED , and the remaining angle CEA D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner it may be demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c . Q. E. D. COR . 1 ...
... angle AED , and the remaining angle CEA D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner it may be demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c . Q. E. D. COR . 1 ...
Σελίδα 39
... angle AEF is greater ( 16. 1. ) than the interior and oppo- site angle EFG ; but it is also equal to it , which is ... remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is ...
... angle AEF is greater ( 16. 1. ) than the interior and oppo- site angle EFG ; but it is also equal to it , which is ... remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...
Σελίδα 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 292 - 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 308 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 39 - 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 too interior angles upon the same side together equal to two right angles.