## 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 twelfthJ. Nourse, London, and J. Balfour, Edinburgh, 1775 - 520 páginas |

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**circle ABC**a straight line is placed**equal**to the**given**straight line D , which is not greater than the diameter of the**circle**. Which was to be done . PROP . II . PRO B. IN a**given circle**to inscribe a**triangle equiangular to a given**... Página 104

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**Let ABC be the given circle , and DEF the given triangle**; it is required to infcribe in the**circle ABC**a**triangle**equiangu- lar to the**triangle DEF**. a Draw the ftraight line GAH touching the**circle**in the point A , and at the point A ... Página 117

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**given circle**ABCDEF . Which was to be done . COR . From this it is manifeft , that the fide of the hexagon is**equal**...**triangle**infcribed in a 2 , 4 . the**circle**, and AR the fide of an**equilateral**and**equiangular**pentagon infcribed in ... Página 194

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**Let ABC**be a**triangle**, and**let**the**angle**BAC be bifected by the ftraight line AD ; the rectangle BA , AC is**equal**to the rectangle BD , DC , together with the fquare of AD . B A C D ...**circle**ACB about the**triangle**, and 194 THE ELEMENTS. Página 438

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**given**ratio to one another ; the**triangle ABC**is**given**in fpecies .**Let**AB be greater than AC , and make the**angle**CAE**equal**to the**angle ABC**; and because the**angle**AEB is com 44. 6. mon to the**triangles**ABE , CAE , they are a**equiangular**...### Otras ediciones - Ver todas

### Términos y frases comunes

alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fhall fhewn fide BC fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles thefe THEOR theſe triangle ABC vertex wherefore

### Pasajes populares

Página 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...

Página 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.

Página 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.

Página 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...

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.