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 TrigonometryW. E. Dean, 1835 - 316 páginas |
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Página 23
... divided into as many trian- gles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are equal to twice as ...
... divided into as many trian- gles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are equal to twice as ...
Página 24
... divided into four triangles , which contain eight right angles ; that is , as many times two right angles as there are units in the number of sides diminished by two . But to avoid all ambiguity , we shall henceforth limit our reasoning ...
... divided into four triangles , which contain eight right angles ; that is , as many times two right angles as there are units in the number of sides diminished by two . But to avoid all ambiguity , we shall henceforth limit our reasoning ...
Página 33
... ed into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . V. PROB . To bisect a given finite 5 OF GEOMETRY . 33 BOOK I.
... ed into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . V. PROB . To bisect a given finite 5 OF GEOMETRY . 33 BOOK I.
Página 34
... divided into two equal parts in the point D. PROP . VI . PROB . C A D B 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 C a point given in it ...
... divided into two equal parts in the point D. PROP . VI . PROB . C A D B 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 C a point given in it ...
Página 45
... divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles con- tained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let ...
... divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles con- tained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 46 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 39 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 47 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 25 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Página 5 - 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 75 - 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 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 52 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Página 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.