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 Trigonometry |
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Page i
... drawn from other sources . By John D. Ogilby . 12mo . ADAMS ' LATIN GRAMMAR ; containing the ancient and modern Pronunciation of the Latin Language ; together with Obser- vations on the Declinable Parts of Speech , Rules for the ...
... drawn from other sources . By John D. Ogilby . 12mo . ADAMS ' LATIN GRAMMAR ; containing the ancient and modern Pronunciation of the Latin Language ; together with Obser- vations on the Declinable Parts of Speech , Rules for the ...
Page 19
... drawn from a cer- tain point within the figure to the circumference , are equal to one another . XII . And this point is called the centre of the circle . XIII . A diameter of a circle is a straight line drawn through the centre , and ...
... drawn from a cer- tain point within the figure to the circumference , are equal to one another . XII . And this point is called the centre of the circle . XIII . A diameter of a circle is a straight line drawn through the centre , and ...
Page 22
... draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line ; it is re- quired to draw , from the point A , a straight line equal to BC . From the point A to B draw , ( 1. Post . ) the ...
... draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line ; it is re- quired to draw , from the point A , a straight line equal to BC . From the point A to B draw , ( 1. Post . ) the ...
Page 23
... drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given ... draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post ...
... drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given ... draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post ...
Page 28
... draw a straight line from the point C at right angles to AB . Take any point D in AC , and ( 3. 1. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equilateral triangle DFE , and join FC ; the straight line FC , drawn from the ...
... draw a straight line from the point C at right angles to AB . Take any point D in AC , and ( 3. 1. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equilateral triangle DFE , and join FC ; the straight line FC , drawn from the ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...