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 18
Hence every equilateral triangle is also equiangular . .PROP . VI . THEOR . F two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles shall be equal to one another .
Hence every equilateral triangle is also equiangular . .PROP . VI . THEOR . F two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles shall be equal to one another .
Seite 19
Hence every equiangular triangle is also equilateral . PRO P. VII . THE O R. U here PON the same base , and on the same side of it , See Ni there cannot be two triangles that have their sides which are terminated in one extremity of the ...
Hence every equiangular triangle is also equilateral . PRO P. VII . THE O R. U here PON the same base , and on the same side of it , See Ni there cannot be two triangles that have their sides which are terminated in one extremity of the ...
Seite 103
... which is not greater than the diameter of the circle . Which was to be done , PRO P. II . PRO B. IN a given circle to inscribe a triangle equiangular to a given triangle . G Let Book IV . a 17 S. b 23. 1 . OF EUCLID . 103.
... which is not greater than the diameter of the circle . Which was to be done , PRO P. II . PRO B. IN a given circle to inscribe a triangle equiangular to a given triangle . G Let Book IV . a 17 S. b 23. 1 . OF EUCLID . 103.
Seite 104
Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe in the circle ABC à triangle equiangular to the triangle DEF . Draw a the straight line GAH touching the circle in the point A , and at the point A ...
Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe in the circle ABC à triangle equiangular to the triangle DEF . Draw a the straight line GAH touching the circle in the point A , and at the point A ...
Seite 105
... and therefore the remaining angle MLN is equal to the c 32 , 1 . remaining angle EDF : Wherefore the triangle LMN is equiangular to the triangle DEF : And it is described about the circle ABC . Which was to be done . PRO P. IV .
... and therefore the remaining angle MLN is equal to the c 32 , 1 . remaining angle EDF : Wherefore the triangle LMN is equiangular to the triangle DEF : And it is described about the circle ABC . Which was to be done . PRO P. IV .
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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 |