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 TrigonometryLippincott, Grambo & Company, 1854 - 317 σελίδες |
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Σελίδα 15
... 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 the angle ACB ; the side AB is also ...
... 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 the angle ACB ; the side AB is also ...
Σελίδα 19
... THEOR . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . Let the straight line AB make with CD , upon one side of it the angles CBA ...
... THEOR . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . Let the straight line AB make with CD , upon one side of it the angles CBA ...
Σελίδα 20
... THEOR . If two straight lines cut one another , the vertical , or opposite angles are equal . Let the two straight lines AB , CD , cut one another in the point E : the angle AEC shall be equal to the angle DEB , and CEB to AED . a For ...
... THEOR . If two straight lines cut one another , the vertical , or opposite angles are equal . Let the two straight lines AB , CD , cut one another in the point E : the angle AEC shall be equal to the angle DEB , and CEB to AED . a For ...
Σελίδα 21
... THEOR . E G F 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 . Produce BC to D ; and because ACD is the exterior angle of ...
... THEOR . E G F 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 . Produce BC to D ; and because ACD is the exterior angle of ...
Σελίδα 22
... THEOR . The greater angle of every triangle is subtended by the greater side , or hus the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than ...
... THEOR . The greater angle of every triangle is subtended by the greater side , or hus the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than ...
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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 Let the straight 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 touches the circle triangle ABC triangle DEF wherefore