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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Página 59
... because AC is equal to CE , the angle EAC is equal to the angle AEC ; and because the angles . ACE is a right angle , the two others AEC , EAC together make one right angled ; and they are equal to one another ; d 32.1 . each of them ...
... because AC is equal to CE , the angle EAC is equal to the angle AEC ; and because the angles . ACE is a right angle , the two others AEC , EAC together make one right angled ; and they are equal to one another ; d 32.1 . each of them ...
Página 111
... angle CBD , because the fide AD Book IV . is equal to the fide AB ; therefore CBD , or DBA is equal to BCD ; and confequently the three angles BDA , DBA , BCD , are g5 .. equal to one another ; and because the angle DBC is equal to the ...
... angle CBD , because the fide AD Book IV . is equal to the fide AB ; therefore CBD , or DBA is equal to BCD ; and confequently the three angles BDA , DBA , BCD , are g5 .. equal to one another ; and because the angle DBC is equal to the ...
Página 161
... angle AFC is equal to the outward angle EAD , and the angle ACF to the ... because the angles ABC , ACB are together less than two right Tangles b ... because the angle ABC is equal to the angle DCE , BF is pa- rallel d to CD ...
... angle AFC is equal to the outward angle EAD , and the angle ACF to the ... because the angles ABC , ACB are together less than two right Tangles b ... because the angle ABC is equal to the angle DCE , BF is pa- rallel d to CD ...
Página 162
... angle EGF , and the triangle ABC is therefore equiangu- lar to the triangle GEF ; and confequently they have their fides oppofite to the equal an- gles proportionals : Where- fore , as AB to BC , so is GE B E C G to EF ; but as AB to BC ...
... angle EGF , and the triangle ABC is therefore equiangu- lar to the triangle GEF ; and confequently they have their fides oppofite to the equal an- gles proportionals : Where- fore , as AB to BC , so is GE B E C G to EF ; but as AB to BC ...
Página 164
... angle in the one equal to one angle in the other , viz . the angle BAC to the angle EDF , and the fides about two other angles ABC , DEF pro- portionals , so that AB is to BC , as DE to EF ; and , in the first cafe , let each of the ...
... angle in the one equal to one angle in the other , viz . the angle BAC to the angle EDF , and the fides about two other angles ABC , DEF pro- portionals , so that AB is to BC , as DE to EF ; and , in the first cafe , let each of the ...
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Términos y frases comunes
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle 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 fide BC fides 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 ſpherical ſquare of AC THEOR theſe thoſe 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.