The Elements of Euclid, Viz: 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. the first six books, together with the eleventh and twelfth |
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Seite 125
I the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , these shall be equimaltiples the one of the second , and the other of the fourth .
I the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , these shall be equimaltiples the one of the second , and the other of the fourth .
Seite 126
THE O R. Sec N. IN F the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third fhall have the fame ratio to any equimultiples of the second ...
THE O R. Sec N. IN F the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third fhall have the fame ratio to any equimultiples of the second ...
Seite 127
ples whatever of the first and third have the same ratio to the Book V. fecond and fourth : And in like manner , the first and the third have the same ratio to any equimultiples whatever of the second and fourth .
ples whatever of the first and third have the same ratio to the Book V. fecond and fourth : And in like manner , the first and the third have the same ratio to any equimultiples whatever of the second and fourth .
Seite 129
Book V. PRO P. A. THE O R. Tf the the first of four magnitudes has to the second , the see N. same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also greater than the fourth ...
Book V. PRO P. A. THE O R. Tf the the first of four magnitudes has to the second , the see N. same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also greater than the fourth ...
Seite 130
C. THE O R. See N. TF the firft be the same multiple of the second , or the fame part of it , that the third is of the fourth ; the first is to the second , as the third is to the fourth . a Let the first A be the same multiple of B the ...
C. THE O R. See N. TF the firft be the same multiple of the second , or the fame part of it , that the third is of the fourth ; the first is to the second , as the third is to the fourth . a Let the first A be the same multiple of B the ...
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added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder definition demonſtrated deſcribed diameter divided double draw drawn equal equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane produced prop proportionals propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid angle ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole
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Seite 32 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.
Seite 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...
Seite 55 - 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 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Seite 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.
Seite 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.
Bibliografische Informationen
| Titel | The Elements of Euclid, Viz: 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. the first six books, together with the eleventh and twelfth |
| Autor/in | Robert Simson |
| Verlag | J. Nourse, London, and J. Balfour, Edinburgh, 1775 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 520 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |