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 15
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle ... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle ... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to ...
Seite 16
... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from ... remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the ...
... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from ... remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the ...
Seite 24
... angle ACD is greater than either of the interior op- posite angles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE ... remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ...
... angle ACD is greater than either of the interior op- posite angles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE ... remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ...
Seite 33
... angles ; the angles AGH , BGH are equal to the angles BGH , GHD : take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD ...
... angles ; the angles AGH , BGH are equal to the angles BGH , GHD : take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD ...
Seite 43
... angle D. Which was to be done . PROP . XLIII . THEOR . THE Complements of the parallelograms which are about the ... remaining com- plement BK is equal to the remaining complement KD . Where- fore the complements , & c . Q. E D. PROP ...
... angle D. Which was to be done . PROP . XLIII . THEOR . THE Complements of the parallelograms which are about the ... remaining com- plement BK is equal to the remaining complement KD . Where- fore the complements , & c . Q. E D. PROP ...
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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 |
Häufige Begriffe und Wortgruppen
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.