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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 15
... 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 the angle ACB ; the side AB ...
... 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 the angle ACB ; the side AB ...
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 . 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 ...
... PROP . XVII . THEOR . 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 ...
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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 definition 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 line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane 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 spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 41 - 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 70 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Σελίδα 91 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 273 - 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 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...