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 sider |
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Resultat 1-5 av 27
Side 31
... angles . COR . 2. And hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be produced , the exterior angle is ...
... angles . COR . 2. And hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be produced , the exterior angle is ...
Side 32
... angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) than the interior and op- posite angle ABC ; to each of these add the angle ACB ...
... angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) than the interior and op- posite angle ABC ; to each of these add the angle ACB ...
Side 34
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ... exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the ...
... angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to ... exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the ...
Side 38
... angle GCB is equal to the angle DFE , but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the ... exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA , which is impossible ( 16. 1 ...
... angle GCB is equal to the angle DFE , but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the ... exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA , which is impossible ( 16. 1 ...
Side 39
... two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH , GHD are equal to one another ; and 1 the exterior angle EGB is equal to the interior OF GEOMETRY . 39 BOOK I.
... two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH , GHD are equal to one another ; and 1 the exterior angle EGB is equal to the interior OF GEOMETRY . 39 BOOK I.
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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...