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 117
... multiple of a less , when the -greater is measured by the less , that is , ' when the greater contains the less a ... multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal to that of the ...
... multiple of a less , when the -greater is measured by the less , that is , ' when the greater contains the less a ... multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal to that of the ...
Side 118
... multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ...
... multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ...
Side 121
... multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . If any number of magnitudes be equimultiples of as IF many , each of each ; what multiple soever any one of them is of its ...
... multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . If any number of magnitudes be equimultiples of as IF many , each of each ; what multiple soever any one of them is of its ...
Side 122
... multiple of the se- cond that the third is of the fourth , and the fifth the same multiple of the second that the sixth is ofthe fourth ; then shall the first together with the fifth be the same multiple of the second , that the third ...
... multiple of the se- cond that the third is of the fourth , and the fifth the same multiple of the second that the sixth is ofthe fourth ; then shall the first together with the fifth be the same multiple of the second , that the third ...
Side 123
... multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF , GH be taken : then EF is the same multiple of B , that GH is of D. Because EF is the same multiple of A , that GH is of C , there ...
... multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF , GH be taken : then EF is the same multiple of B , that GH is of D. Because EF is the same multiple of A , that GH is of C , there ...
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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.