The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock1852 |
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Página 59
... two equal parts . Q. E. D. [ The same should , for the sake of practice , be proved with the accom- panying figure . ] B PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another .
... two equal parts . Q. E. D. [ The same should , for the sake of practice , be proved with the accom- panying figure . ] B PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another .
Página 62
... Triangles upon the same base , and between the same paral- lels , are equal to one another . Let the triangles ABC , DBC be upon the same base BC , and between the same parallels AD , BC : The triangle ABC is equal to the triangle DBC ...
... Triangles upon the same base , and between the same paral- lels , are equal to one another . Let the triangles ABC , DBC be upon the same base BC , and between the same parallels AD , BC : The triangle ABC is equal to the triangle DBC ...
Página 64
... same base , and upon the same side of it , are between the same parallels . Let the equal triangles ... 1. through the point A drawa AE parallel to BC , and join EC : b xxxvii . 1 ... other line but AD is parallel to BC ; AD is therefore ...
... same base , and upon the same side of it , are between the same parallels . Let the equal triangles ... 1. through the point A drawa AE parallel to BC , and join EC : b xxxvii . 1 ... other line but AD is parallel to BC ; AD is therefore ...
Página 66
... between the same parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; a * xxxvii . 1. then the triangle ABC is equal to the triangle EBC , A D E because they are upon the same base BC , and between the same ...
... between the same parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; a * xxxvii . 1. then the triangle ABC is equal to the triangle EBC , A D E because they are upon the same base BC , and between the same ...
Página 67
... one of its angles equal to a given rectilineal angle . Let ABC be the given triangle , and D the given rectilineal ... upon equal bases BE , B EC ; and between the same parallels BC , AG : A F N G therefore the triangle ABC is double of the ...
... one of its angles equal to a given rectilineal angle . Let ABC be the given triangle , and D the given rectilineal ... upon equal bases BE , B EC ; and between the same parallels BC , AG : A F N G therefore the triangle ABC is double of the ...
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The First Two Books of the Elements of Euclid, with Additional Figures ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 18 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 11 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 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.