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 sider |
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Resultat 1-5 av 45
Side 9
... angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or ... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the ...
... angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or ... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the ...
Side 13
... angles ABC , ABD are likewise together equal to two right an- gles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ...
... angles ABC , ABD are likewise together equal to two right an- gles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ...
Side 14
... angle ACD is greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the ... remaining angles to the remaining angles each to each , to which the equal sides are opposite ; wherefore the angle BAE ...
... angle ACD is greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the ... remaining angles to the remaining angles each to each , to which the equal sides are opposite ; wherefore the angle BAE ...
Side 20
... angles , and AGH , BGH , are also equal ( 6.1 . ) to two right angles , the angles AGH , BGH are equal to the angles BGH , E A Ꮐ B C H D GHD : Take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining ...
... angles , and AGH , BGH , are also equal ( 6.1 . ) to two right angles , the angles AGH , BGH are equal to the angles BGH , E A Ꮐ B C H D GHD : Take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining ...
Side 25
... angles ABC , BCD are equal ( 21. 1. ) ; and because AB is equal to CD , and BC com- mon to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ... remaining sides will also be equal and parallel ...
... angles ABC , BCD are equal ( 21. 1. ) ; and because AB is equal to CD , and BC com- mon to the two triangles ABC , DCB , the two sides AB , BC are equal to the two DC , CB ; and the angle ... remaining sides will also be equal and parallel ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |
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 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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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...
Side 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.