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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Page 10
... 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 somewhere upon one of those straight lines , and 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 somewhere upon one of those straight lines , and the ...
Page 19
... vertex of each of the tri- angles is without the other triangle , because AC is equal to AD , the angle ACD is equal to the angle ADC : But the angle ACD is greater than the angle BCD ; therefore the angle A ADC is greater also than BCD ...
... vertex of each of the tri- angles is without the other triangle , because AC is equal to AD , the angle ACD is equal to the angle ADC : But the angle ACD is greater than the angle BCD ; therefore the angle A ADC is greater also than BCD ...
Page 38
... 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 fides . a . 2. Cor . 15. 1 . Cor ...
... 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 fides . a . 2. Cor . 15. 1 . Cor ...
Page 155
... to the greater segment , as the greater seg- ment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the bafe . PROP . Book VL See N. a 38. 1 . T PROP 155 ...
... to the greater segment , as the greater seg- ment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the bafe . PROP . Book VL See N. a 38. 1 . T PROP 155 ...
Page 158
... vertex to the point of section , di- vides the vertical angle into two equal angles . Let the angle BAC of any triangle ABC be divided into two equal angles by the straight line AD : BD is to DC , as BA to AC . Thro : Thro ' the point C ...
... vertex to the point of section , di- vides the vertical angle into two equal angles . Let the angle BAC of any triangle ABC be divided into two equal angles by the straight line AD : BD is to DC , as BA to AC . Thro : Thro ' the point C ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.