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 TrigonometryMarot & Walter, 1826 - 320 sider |
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Resultat 1-5 av 68
Side 31
... bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be the given rectilineal ... bisected by the straight line AF . Which was to be done . PROP . X. PROB . To bisect a given finite straight line ...
... bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be the given rectilineal ... bisected by the straight line AF . Which was to be done . PROP . X. PROB . To bisect a given finite straight line ...
Side 32
... bisect the angle ACB by the straight line CD . AB is cut into two equal parts in the point D. C Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; the two sides AC , CD , are equal to the two BC , CD , each to ...
... bisect the angle ACB by the straight line CD . AB is cut into two equal parts in the point D. C Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; the two sides AC , CD , are equal to the two BC , CD , each to ...
Side 33
... bisect FG in H , and join CF , CH , CG ; the straight b , 10. 1 . line CH , drawn from the given point C , is perpendicular to the given straight line AB . с 1 . Because FH is equal to HG , and HC common to the two triangles FHC , GHC ...
... bisect FG in H , and join CF , CH , CG ; the straight b , 10. 1 . line CH , drawn from the given point C , is perpendicular to the given straight line AB . с 1 . Because FH is equal to HG , and HC common to the two triangles FHC , GHC ...
Side 36
... bisected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c . Q , E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two ...
... bisected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c . Q , E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two ...
Side 70
... 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 of half the line bisected , is equal to the square of the straight line which is ...
... 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 of half the line bisected , is equal to the square of the straight line which is ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1826 |
Elements of Geometry: Containing the First Six Books of Euclid; With Two ... Formerly Chairman Department of Immunology John Playfair Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected Book centre circle ABC circumference cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line gles greater hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle right angled triangle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line AC Supplement THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 233 - But because the triangle KGN is isosceles, the angle GKN is equal to the angle GNK, and the angles GMK, GMN are both right angles by construction ; wherefore, the triangles GMK, GMN have two angles of the one equal to two angles of the other, and they have also the side GM common, therefore they
Side 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. VIII. An obtuse angle is that which is greater than a right angle.
Side 77 - AB is divided in H, so that the rectangle AB, BH is equal to the square of AH. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal
Side 69 - 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. Let the straight line AB be divided into two equal parts in the
Side 48 - PROP. XXX. THEOR. Straight lines which are parallel to the same straight line are parallel to one another. Let AB, CD, be each of them parallel to EF; AB is also parallel to CD. Let the straight line GHK cut AB, EF, CD ; and because GHK cuts the parallel straight lines
Side 32 - 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 Ca point given in it; it is required to draw a straight line from the point C at right angles to AB.
Side 75 - PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square* of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half
Side 18 - taken, the straight line between them lies wholly in that superficies. VI. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. E NB ' When several angles are at one point B, any one of them is
Side 153 - Therefore, &c. QED PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and fourth; the multiple
Side 50 - angles. Therefore, twice as many right angles as the figure has sides, are equal to all the angles of the figure, together with four right angles, that is, the angles of the figure are equal to twice as many right angles as the figure has sides, wanting four. Because every interior angle ABC, with its adjacent exterior ABD, is