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 páginas |
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Página iv
... thing new in Elementary Geometry would have been soon attempted . But his design was different : it was his object to re- store the writings of EUCLID to their original per- fection , and to give them to modern Europe as nearly as ...
... thing new in Elementary Geometry would have been soon attempted . But his design was different : it was his object to re- store the writings of EUCLID to their original per- fection , and to give them to modern Europe as nearly as ...
Página vi
... thing from the rigour of geome- trical demonstration . By this means , the steps of the reasoning which were before far separated , are brought near to one another , and the force of the whole is so clearly and directly perceived , that ...
... thing from the rigour of geome- trical demonstration . By this means , the steps of the reasoning which were before far separated , are brought near to one another , and the force of the whole is so clearly and directly perceived , that ...
Página x
... thing to be done , as any line to be drawn , or any figure to be constructed , the manner of doing which he has not ... thing to be supposed , unless the thing itself be actually exhibited . But it is not always necessary to make use of ...
... thing to be done , as any line to be drawn , or any figure to be constructed , the manner of doing which he has not ... thing to be supposed , unless the thing itself be actually exhibited . But it is not always necessary to make use of ...
Página xi
... things is obviously possible , and very far from implying a contradiction , where the method of actually exhibiting them may be al- together unknown . Thus , it is plain , that on any given figure as a base , a solid may be constituted ...
... things is obviously possible , and very far from implying a contradiction , where the method of actually exhibiting them may be al- together unknown . Thus , it is plain , that on any given figure as a base , a solid may be constituted ...
Página xii
... thing not essential . That it may be the better understood , and because the demonstra- tions which require exhaustions , are , no doubt , the most difficult in the Elements , they are all conduct- ed as nearly as possible in the same ...
... thing not essential . That it may be the better understood , and because the demonstra- tions which require exhaustions , are , no doubt , the most difficult in the Elements , they are all conduct- ed as nearly as possible in the same ...
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Términos y frases comunes
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
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Página 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
Página 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.
Página 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
Página 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
Página 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
Página 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.
Página 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
Página 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
Página 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
Página 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