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 σελίδες |
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Σελίδα 480
... sine CD , and that ex- tremity , is called the Versed Sine of the arch AC , or angle ABC . VI . A straight line AE touching the circle at A , one extremity of the arch AC , and meeting the diameter BC passing through the other extremity ...
... sine CD , and that ex- tremity , is called the Versed Sine of the arch AC , or angle ABC . VI . A straight line AE touching the circle at A , one extremity of the arch AC , and meeting the diameter BC passing through the other extremity ...
Σελίδα 481
... sine , versed sine , tangent , and se- cant , of any arch which is the measure of any given angle ABC , is to the sine , versed sine , tangent , and secant , of any other arch which is the measure of the same angle , as the radius of ...
... sine , versed sine , tangent , and se- cant , of any arch which is the measure of any given angle ABC , is to the sine , versed sine , tangent , and secant , of any other arch which is the measure of the same angle , as the radius of ...
Σελίδα 482
... sine of the angle ABC opposite to it ; and if either side BA be made radius , the other side AC will be the tangent of the angle ABC op- posite to it , and the hypothenuse BC the secant of the same angle . About B as a centre , with BC ...
... sine of the angle ABC opposite to it ; and if either side BA be made radius , the other side AC will be the tangent of the angle ABC op- posite to it , and the hypothenuse BC the secant of the same angle . About B as a centre , with BC ...
Σελίδα 484
... sine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle ABC con- tained by any two sides BA , BC is to the difference of the sum of the squares of BA , BC , and the square of the base AC , as the ...
... sine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle ABC con- tained by any two sides BA , BC is to the difference of the sum of the squares of BA , BC , and the square of the base AC , as the ...
Σελίδα 485
... sine of BAD , which is the complement of the angle ABC , that is , as radius to the co - sine of ABC . PROP . VI . FIG . II . IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half the per ...
... sine of BAD , which is the complement of the angle ABC , that is , as radius to the co - sine of ABC . PROP . VI . FIG . II . IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half the per ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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...
Σελίδα 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.