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 Seiten |
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Seite 15
... equal to AB ; and because the point B is the centre of the 5th De circle ACE , BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal to the fame are ...
... equal to AB ; and because the point B is the centre of the 5th De circle ACE , BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal to the fame are ...
Seite 16
... BC is equal to BG ; and because D is the centre of the circle GKL , DL is equal to DG , and DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder f BG : But it has been shewn , that BC is equal to ...
... BC is equal to BG ; and because D is the centre of the circle GKL , DL is equal to DG , and DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder f BG : But it has been shewn , that BC is equal to ...
Seite 17
... equal A to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are oppofite , shall be equal each to each , viz . the angle ABC to the ...
... equal A to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are oppofite , shall be equal each to each , viz . the angle ABC to the ...
Seite 20
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other fide of the base CD are equal to one another ; but the angle ECD is greater than the angle ... BC BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other fide of the base CD are equal to one another ; but the angle ECD is greater than the angle ... BC BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
Seite 21
... BC is equal to EF ; therefore BC coinciding with EF , BA and Book J. AC shall coincide with ED and DF ; for , if the base BC coin- cides with the base EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a ...
... BC is equal to EF ; therefore BC coinciding with EF , BA and Book J. AC shall coincide with ED and DF ; for , if the base BC coin- cides with the base EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone confequently conſtruction cylinder demonſtration deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fides BA fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs line BC oppoſite parallel parallelepipeds parallelogram paſs perpendicular priſm proportionals propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſolid ſpace ſphere ſquare of AC THEOR theſe thoſe triangle ABC vertex wherefore
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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.