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 TrigonometryCollins and Hannay, 1833 - 333 páginas |
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Página 17
... inclination of two straight lines to one another , which meet together , but are not in the same straight line . * The definitions marked with inverted commas are different from those of Euclid . A D 6 B E C N. B. When several 3.
... inclination of two straight lines to one another , which meet together , but are not in the same straight line . * The definitions marked with inverted commas are different from those of Euclid . A D 6 B E C N. B. When several 3.
Página 18
... meet one another , is put between the other two letters , and one of these two is somewhere upon one of those straight lines , and the other upon the other line : Thus the angle which ' is contained by the straight lines , AB , CB , is ...
... meet one another , is put between the other two letters , and one of these two is somewhere upon one of those straight lines , and the other upon the other line : Thus the angle which ' is contained by the straight lines , AB , CB , is ...
Página 20
... besides these , are called Trapeziums . XXX . Parallel straight lines , are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight 20 ELEMENTS.
... besides these , are called Trapeziums . XXX . Parallel straight lines , are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight 20 ELEMENTS.
Página 38
... meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) 38 ELEMENTS.
... meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) 38 ELEMENTS.
Página 39
... meet towards B , D. In like manner it may be demonstrated that they do not meet towards A , A E B G D C F C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 30. Def . ) to one another . AB ...
... meet towards B , D. In like manner it may be demonstrated that they do not meet towards A , A E B G D C F C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 30. Def . ) to one another . AB ...
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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 centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 49 - PROB. jf 0 a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle, Let AB be the given straight line, and C the given triangle, and D the given rectilineal angle.
Página 29 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Página 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 90 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 86 - 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.
Página 87 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Página 43 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Página 39 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alter' male angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same. side together equal to two right angles.
Página 54 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...