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 Seiten |
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Seite 4
... given of compound ratio , and given an absurd one in place of it in the 5th Definition of the 6th Book , which neither Euclid , Archimedes , Appollonius , nor any geometer before Theon's time , ever made use of , and of which there is ...
... given of compound ratio , and given an absurd one in place of it in the 5th Definition of the 6th Book , which neither Euclid , Archimedes , Appollonius , nor any geometer before Theon's time , ever made use of , and of which there is ...
Seite 173
... given straight line simi- lar to one given , and so on . Which was to be done . PROP . XIX . THEOR . SIMILAR triangles are to one another in the duplicate ratio of their homologous sides . Let ABC , DEF be similar triangles , having the ...
... given straight line simi- lar to one given , and so on . Which was to be done . PROP . XIX . THEOR . SIMILAR triangles are to one another in the duplicate ratio of their homologous sides . Let ABC , DEF be similar triangles , having the ...
Seite 299
... give the reason why two sides of a triangle are greater than the third : but the ... ratio which is less than that of two to one , as Pappus Alexandrinus has ... given , viz . that any two of the straight lines DF , FG , GH must be great ...
... give the reason why two sides of a triangle are greater than the third : but the ... ratio which is less than that of two to one , as Pappus Alexandrinus has ... given , viz . that any two of the straight lines DF , FG , GH must be great ...
Seite 310
... give a general and summary idea of ratio to beginners , by premising this metaphysical definition , to the more accurate defini- tions of ratios that are the same to one another , or one of which is greater , or less than the other : I ...
... give a general and summary idea of ratio to beginners , by premising this metaphysical definition , to the more accurate defini- tions of ratios that are the same to one another , or one of which is greater , or less than the other : I ...
Seite 311
... proportion of numbers to one another is defined , and treated of , yet without giving any definition of the ratio of numbers ; though such a definition was as necessary and useful to be given in that book , as in this : but indeed there ...
... proportion of numbers to one another is defined , and treated of , yet without giving any definition of the ratio of numbers ; though such a definition was as necessary and useful to be given in that book , as in this : but indeed there ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Keine Leseprobe verfügbar - 2018 |
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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
Beliebte Passagen
Seite 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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...
Seite 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.