First principles of Euclid: an introduction to the study of the first book of Euclid's Elements1880 |
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Página 16
... side of it , taken together , less than two right angles , these straight lines , being continually produced , shall at length meet on that side ... A C Lines which are equal coincide ( Axiom 8a ) . A B and CD are equal ( given ) . ( a ) ..
... side of it , taken together , less than two right angles , these straight lines , being continually produced , shall at length meet on that side ... A C Lines which are equal coincide ( Axiom 8a ) . A B and CD are equal ( given ) . ( a ) ..
Página 23
T S. Taylor. ( b ) A C and B C are each equal to A B. Things which are equal to the same thing are equal to one another ( Axiom 1 ) . ( c ) .. A C ... side of the given line I prove that the five sides are all equal ( use figures instead of ...
T S. Taylor. ( b ) A C and B C are each equal to A B. Things which are equal to the same thing are equal to one another ( Axiom 1 ) . ( c ) .. A C ... side of the given line I prove that the five sides are all equal ( use figures instead of ...
Página 30
... AC cut off A E equal to A D. Join DE . ( b ) On DE , on the side remote from A , describe the equilateral triangle DFE . ( Euc . I. I shows how to do this . ) Join A F The line AF shall bisect the angle BA C. B A D If the angle B A C is ...
... AC cut off A E equal to A D. Join DE . ( b ) On DE , on the side remote from A , describe the equilateral triangle DFE . ( Euc . I. I shows how to do this . ) Join A F The line AF shall bisect the angle BA C. B A D If the angle B A C is ...
Página 56
... side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles ... A C , and call the point of intersection E. Join BE . Produce the line BE to F , making EFequal to BE . Join FC . Ist Proof .
... side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles ... A C , and call the point of intersection E. Join BE . Produce the line BE to F , making EFequal to BE . Join FC . Ist Proof .
Página 59
... side A C be produced to G , it may be shown that the angle B C G , that is the angle ACD ( Euc . I. 15 ) , is greater than the angle АВС . Q. E. D. EXERCISES . - I . Prove , as above , that angle B C G ( Fig . 3 ) is greater than angle ...
... side A C be produced to G , it may be shown that the angle B C G , that is the angle ACD ( Euc . I. 15 ) , is greater than the angle АВС . Q. E. D. EXERCISES . - I . Prove , as above , that angle B C G ( Fig . 3 ) is greater than angle ...
Términos y frases comunes
1st conclusion 2nd Syllogism A B equal ABC is equal adjacent angles alternate angle angle A CD angle ABC angle B A C angle BAC angle contained angle DFE angle EDF angle GHD angles BGH angles equal Axiom 2a Axiom 9 base B C bisected CD is greater coincide Construction definition diameter enunciations of Euc equal angles equal to A B equal to angle equal to CD equal to side equilateral triangle EXERCISES.-I exterior angle figure given line given point given straight line greater than angle included angle interior opposite angle isosceles triangle Join Let us suppose line A B line CD major premiss parallel to CD parallelogram Particular Enunciation PROBLEM Euclid produced proposition prove that angle remaining angle Required right angles side A C sides equal square THEOREM Euclid triangle ABC
Pasajes populares
Página 83 - 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 18 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 66 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Página 34 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Página 94 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Página 88 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 104 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 140 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Página 51 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 132 - 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.