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 52
... reason HF also is a square , and it is upon the side HG , which is equal to AC : therefore HF , CK are the squares of AC , CB ; and because the complement AG is equal ( 43.1 . ) to the complement GE , and that AG is the rectangle con ...
... reason HF also is a square , and it is upon the side HG , which is equal to AC : therefore HF , CK are the squares of AC , CB ; and because the complement AG is equal ( 43.1 . ) to the complement GE , and that AG is the rectangle con ...
Side 56
... reason , PR is equal to RO ; and be- cause CB , is equal to BD , and GK to KN , the rectangle CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram CO ...
... reason , PR is equal to RO ; and be- cause CB , is equal to BD , and GK to KN , the rectangle CK is equal ( 36. 1. ) to BN , and GR to RN ; but CK is equal ( 43. 1. ) to RN , because they are the complements of the parallelogram CO ...
Side 57
... reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle : and because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) to the interior and opposite ...
... reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle : and because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) to the interior and opposite ...
Side 58
... ( 32. 1. ) : for the same reason , each of the angles CEB , EBC is half a right angle : therefore AEB is a right angle : and because EBC is half a right angle , DBG is also E 59 F C B D G ( 15. 1. THE ELEMENTS OF EUCLID . BOOK IT .
... ( 32. 1. ) : for the same reason , each of the angles CEB , EBC is half a right angle : therefore AEB is a right angle : and because EBC is half a right angle , DBG is also E 59 F C B D G ( 15. 1. THE ELEMENTS OF EUCLID . BOOK IT .
Side 71
... reason , CF is greater than GF : again , because GF , FE are greater ( 20. 1. ) than EG , and EG , is equal to ED ; GF , FE are greater than ED : take away the common part FE , and the remainder GF is greater than the remainder FD ...
... reason , CF is greater than GF : again , because GF , FE are greater ( 20. 1. ) than EG , and EG , is equal to ED ; GF , FE are greater than ED : take away the common part FE , and the remainder GF is greater than the remainder FD ...
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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
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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.