The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored : Also, the Book of Euclid's Data, in Like Manner Corrected : to this Edition are Also Annexed, Elements of Plane and Spherical TrigonometryRobert Desilver, 1821 - 516 sider |
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Resultat 1-5 av 21
Side 480
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle again ...
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle again ...
Side 481
... radius CB to the radius NB , and AE to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by conversion , DA to MO as AB to MB . Hence the corollary is manifest ; there- fore , if the radius be supposed to be divided into any ...
... radius CB to the radius NB , and AE to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by conversion , DA to MO as AB to MB . Hence the corollary is manifest ; there- fore , if the radius be supposed to be divided into any ...
Side 482
... radius , the sides become the sines of the angles op- posite to them ; and if either side be made radius , the remaining side is the tangent of the angle opposite to it , and the hypothenuse the secant of the same angle . Let ABC be a ...
... radius , the sides become the sines of the angles op- posite to them ; and if either side be made radius , the remaining side is the tangent of the angle opposite to it , and the hypothenuse the secant of the same angle . Let ABC be a ...
Side 483
... radius , BE , BG , are the tangents of the angles EFB , BFG ; but it is manifest that EC is the sum of the sides BA ... radius is to the tangent of an angle , and the radius is to the tangent of the excess of this angle above half a ...
... radius , BE , BG , are the tangents of the angles EFB , BFG ; but it is manifest that EC is the sum of the sides BA ... radius is to the tangent of an angle , and the radius is to the tangent of the excess of this angle above half a ...
Side 484
... radius is to the tangent of the angle ABD ; and because BGD is a right angle , BG is to GD or GF as the radius is to the tangent of GBD , which is the excess of the angle ABD above ABF half a right angle . But because EB is parallel to ...
... radius is to the tangent of the angle ABD ; and because BGD is a right angle , BG is to GD or GF as the radius is to the tangent of GBD , which is the excess of the angle ABD above ABF half a right angle . But because EB is parallel to ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
AC is equal altitude angle ABC angle BAC base BC BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar solid angle solid parallelopipeds sphere spherical angle square of AC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Populære avsnitt
Side 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Side 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 9 - 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, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 53 - 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 of the line between the points of section, is equal to the square of half the line.
Side 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 21 - 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 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.