First principles of Euclid: an introduction to the study of the first book of Euclid's Elements1880 |
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Page 12
... and AC are equal . B Major Premiss . A Minor Premiss . AB and CD C are parallel lines . B D Conclusion ... A B and CD if produced will never meet . Major Premiss . Minor Premiss . The line CD stand- 12 First Principles of Euclid .
... and AC are equal . B Major Premiss . A Minor Premiss . AB and CD C are parallel lines . B D Conclusion ... A B and CD if produced will never meet . Major Premiss . Minor Premiss . The line CD stand- 12 First Principles of Euclid .
Page 16
... produced , shall at length meet on that side on which are the angles that are less than two right angles ( See page 100 , Part III . ) . A CHAIN OF SYLLOGISMS . The conclusion of one syllogism may become the premiss of a second ...
... produced , shall at length meet on that side on which are the angles that are less than two right angles ( See page 100 , Part III . ) . A CHAIN OF SYLLOGISMS . The conclusion of one syllogism may become the premiss of a second ...
Page 27
... produced ever so far in the direction of B and C without increasing the size of the angle . To compare one triangle with another , we must apply one to the other . B D F Thus , to compare the angle B A C with the angle EDF ; apply the ...
... produced ever so far in the direction of B and C without increasing the size of the angle . To compare one triangle with another , we must apply one to the other . B D F Thus , to compare the angle B A C with the angle EDF ; apply the ...
Page 38
... ( produce NO towards N ) . III . At the point N in the straight line given in ( II ) , draw a straight line double the length of NO at right angles to NO . ( Produce NO both ways ; make the produced parts each equal to NO ; draw a line at ...
... ( produce NO towards N ) . III . At the point N in the straight line given in ( II ) , draw a straight line double the length of NO at right angles to NO . ( Produce NO both ways ; make the produced parts each equal to NO ; draw a line at ...
Page 41
... produce ( 2 , 3 ) both ways to cut the circle . ) III . From the point O draw a perpendicular to the line PQ . 2 3 P 0 PROBLEM ( Euclid I. 23 ) . Repeat the enunciation of Euc . I. 8 ( page 46 ) . General Enunciation . At a given point ...
... produce ( 2 , 3 ) both ways to cut the circle . ) III . From the point O draw a perpendicular to the line PQ . 2 3 P 0 PROBLEM ( Euclid I. 23 ) . Repeat the enunciation of Euc . I. 8 ( page 46 ) . General Enunciation . At a given point ...
Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.