The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock1852 |
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Side 17
... likewise equal to AD ; whence AE and C are each of them equal to AD ; wherefore the straight line AE is equal to C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less . Which was to be done ...
... likewise equal to AD ; whence AE and C are each of them equal to AD ; wherefore the straight line AE is equal to C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less . Which was to be done ...
Side 18
... likewise the angles con- tained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
... likewise the angles con- tained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
Side 19
... likewise the angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ...
... likewise the angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ...
Side 23
... likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ACB , ADB , upon the same base AB , and upon the same side of it , which have their sides CA , DA , terminated in the extremity ...
... likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ACB , ADB , upon the same base AB , and upon the same side of it , which have their sides CA , DA , terminated in the extremity ...
Side 24
... likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD ; Again , because CB is equal to DB , a v . 1 . a the angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ...
... likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD ; Again , because CB is equal to DB , a v . 1 . a the angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ...
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The First Two Books of the Elements of Euclid, with Additional Figures ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
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adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angled triangle angles CBA angles equal Arithmetic base BC BC is equal bisected BOOK bound centre cloth coincide Delectus diameter double English Notes equal to BC equal to twice Eton Eton College Euclid's Elements Exercises exterior angle four right angles Geography given point given rectilineal angle given straight line gnomon greater Greek half a right interior and opposite isosceles JANE MARCET join Let ABC Let the straight Lexicon M.A. New Edition Maps opposite angle parallel to CD parallelogram perpendicular Post 8vo produced Proposition rectangle BC rectangle contained rectilineal figure remaining angle rhombus right angles Schools Shrewsbury School sides BA sides equal square described square of AC THEOR triangle ABC twice the rectangle VALPY Valpy's wherefore xxxi
Populære avsnitt
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 67 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 51 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 109 - ... subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn perpendicular to BC produced.
Side 12 - Mrs. R. Lee's Elements of Natural History ; or, First Principles of Zoology : Comprising the Principles of Classification, interspersed with amusing and instructive Accounts of the most remarkable Animals.
Side 53 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Side 76 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 34 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. And in like manner, it may be demonstrated, that no other can be in the same straight line with it but BD, which therefore is in the same straight line with CB.
Side 11 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 37 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.