Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical GeometryW. E. Dean, 1845 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 99.
Σελίδα 8
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , * The definitions marked with inverted commas are different from those of Euclid ...
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , * The definitions marked with inverted commas are different from those of Euclid ...
Σελίδα 13
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , AA F viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to ...
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , AA F viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to ...
Σελίδα 14
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , SO that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , SO that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
Σελίδα 15
... triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to ...
... triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to ...
Σελίδα 16
... angle which is contain- ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
... angle which is contain- ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 50 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 16 - If two triangles have two sides of the one equal to two sides of the other...
Σελίδα 28 - 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 angle upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 13 - From the greater of two given straight lines to cut off a part equal to the less.
Σελίδα 9 - 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 52 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 149 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 30 - 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 21 - Any two angles of a triangle are together less than two right angles, Let ABC be any triangle ; any two of its angles together are less than two right angles.