## 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 sider |

### Fra bogen

Resultater 1-5 af 29

Side 26

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**bifected**, it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . Therefore , if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angles of a triangle are together less than two ... Side 56

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**bifected**, and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the fquare of half of the line**bifected**, is equal to the fquare of the ftraight line which is ... Side 60

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**bifected**, and of the fquare of the line made up of the half and the part pro- duced . Let the ftraight line AB be**bifected**in C , and produced to the point D ; the fquares of AD , DB are double of the fquares of AC , CD . From the ... Side 62

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**bifected**in E , and produced to the point F , the rectangle CF , FA , to- gether with the fquare of AE , is equal d to the fquare of EF : But EF is equal to EB ; therefore the rectangle CF , FA , toge- ther with the fquare of AE , is ... Side 70

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**bifect**it . Let ABC be a circle ; and let CD , a ftraight line drawn through the center**bifect**any straight line AB , which does not pafs through the center , in the point F : It cuts it also at right angles . Take 2 E the center of the ...### Andre udgaver - Se alle

### Almindelige termer og sætninger

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### Populære passager

Side 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...

Side 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.

Side 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.

Side 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...

Side 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.

Side 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.

Side 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.

Side 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.

Side 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.

Side 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.