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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Side 4
... magnitude . Now this Pro- position is a Theorem ; not a Definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and therefore , though this were a true Proposition , it ought to have been ...
... magnitude . Now this Pro- position is a Theorem ; not a Definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and therefore , though this were a true Proposition , it ought to have been ...
Side 117
... magnitude is said to be a part of a greater magnitude , when the less measures the greater , that is , when the less is contained a certain number of times exactly in the greater . ' II . A greater magnitude is said to be a multiple of ...
... magnitude is said to be a part of a greater magnitude , when the less measures the greater , that is , when the less is contained a certain number of times exactly in the greater . ' II . A greater magnitude is said to be a multiple of ...
Side 120
... magnitudes are taken two and two . ' XIX . Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank : ' as the first to the second of the other rank : and as the second ...
... magnitudes are taken two and two . ' XIX . Ex æquali , from equality ; this term is used simply by itself , when the first magnitude is to the second of the first rank : ' as the first to the second of the other rank : and as the second ...
Side 121
... magnitude is greater than the same mul- tiple of a less . IV . That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . If any number of magnitudes be ...
... magnitude is greater than the same mul- tiple of a less . IV . That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . If any number of magnitudes be ...
Side 122
... magnitudes be of all the other : ' For the same demonstration holds in any number of magnitudes , which was here applied ' to two . ' Q. E. D. PROP . II . THEOR . IF the first magnitude be the same multiple of the se- cond that the ...
... magnitudes be of all the other : ' For the same demonstration holds in any number of magnitudes , which was here applied ' to two . ' Q. E. D. PROP . II . THEOR . IF the first magnitude be the same multiple of the se- cond that the ...
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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.