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 74
Side vi
... near to one another , and the force of the whole is so clearly and directly perceived , that I am persuaded no more difficulty will be found in un- 1 derstanding the propositions of the Fifth Book , than those vi PREFACE .
... near to one another , and the force of the whole is so clearly and directly perceived , that I am persuaded no more difficulty will be found in un- 1 derstanding the propositions of the Fifth Book , than those vi PREFACE .
Side x
... whole of the Elements , viz . That , in the demon- stration of a theorem , he never supposes any thing to be done , as any line to be drawn , or any figure to be constructed , the manner of doing which he has not previously explained ...
... whole of the Elements , viz . That , in the demon- stration of a theorem , he never supposes any thing to be done , as any line to be drawn , or any figure to be constructed , the manner of doing which he has not previously explained ...
Side 23
... whole is greater than its part . X. All right angles are equal to one another . XI . " Two straight lines which intersect one another , cannot " be both parallel to the same straight line . ” Book I. late . PROPOSITION I. PROBLEM . To ...
... whole is greater than its part . X. All right angles are equal to one another . XI . " Two straight lines which intersect one another , cannot " be both parallel to the same straight line . ” Book I. late . PROPOSITION I. PROBLEM . To ...
Side 26
... whole triangle ABC shall coincide with the whole tri- * The three conclusions in this enunciation are more briefly expressed by saying , that the triangles are in every way equal . b 3. Ax . angle DEF , so that the 26 ELEMENTS.
... whole triangle ABC shall coincide with the whole tri- * The three conclusions in this enunciation are more briefly expressed by saying , that the triangles are in every way equal . b 3. Ax . angle DEF , so that the 26 ELEMENTS.
Side 27
... whole AF is equal to the whole AG , and the part AB to the part AC ; the remainder BF is e- D F N. a 3. 1 . b 4. 1 . B C G E a 3. Ax . b 4. 1 . Book I. OF GEOMETRY . 27.
... whole AF is equal to the whole AG , and the part AB to the part AC ; the remainder BF is e- D F N. a 3. 1 . b 4. 1 . B C G E a 3. Ax . b 4. 1 . Book I. OF GEOMETRY . 27.
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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