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 13
... PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
... PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
Σελίδα 17
... PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE ...
... PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE ...
Σελίδα 18
... PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi red to draw a straight line from the point ...
... PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi red to draw a straight line from the point ...
Σελίδα 20
... PROP . XV . 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 ...
... PROP . XV . 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 ...
Σελίδα 21
... PROP . XVII . 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 ...
... PROP . XVII . 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 ...
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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