First principles of Euclid: an introduction to the study of the first book of Euclid's Elements1880 |
Inni boken
Resultat 6-10 av 19
Side 79
... base of the one with the greater angle shall be greater than the base of the other . The same , in tabular form ... B C is greater than the base E F Construction . In the triangle DEF ( Fig . 1 ) the two sides are DE and DF . Of those ...
... base of the one with the greater angle shall be greater than the base of the other . The same , in tabular form ... B C is greater than the base E F Construction . In the triangle DEF ( Fig . 1 ) the two sides are DE and DF . Of those ...
Side 81
... base E G is greater than base E F. But E G is equal to B C ( h ) . ... base B C is greater than base E F. Q. E. D. EXERCISES . - I . Draw the triangles A B C , DEF ( Fig . 2 ) , with A B , A C , DE , D F , all equal . II . In Fig . 2 ...
... base E G is greater than base E F. But E G is equal to B C ( h ) . ... base B C is greater than base E F. Q. E. D. EXERCISES . - I . Draw the triangles A B C , DEF ( Fig . 2 ) , with A B , A C , DE , D F , all equal . II . In Fig . 2 ...
Side 82
... base of the one greater than the base of the other ; the angle contained by the sides of that which has the greater ... BC greater than EF ― Required . To prove that angle B A C is greater than angle EDF . Proof . The angle B A C must be ...
... base of the one greater than the base of the other ; the angle contained by the sides of that which has the greater ... BC greater than EF ― Required . To prove that angle B A C is greater than angle EDF . Proof . The angle B A C must be ...
Side 86
... BC is equal to EF , and the included angle ABC is equal to the included angle DEF ( Given a ) . .. ( by Euc . I. 4 ) the base AC is equal to the base D F , and the remaining angle BAC is equal to the remaining angle Q. E. D. EDF . CASE ...
... BC is equal to EF , and the included angle ABC is equal to the included angle DEF ( Given a ) . .. ( by Euc . I. 4 ) the base AC is equal to the base D F , and the remaining angle BAC is equal to the remaining angle Q. E. D. EDF . CASE ...
Side 87
... base AC is equal to base DF , and angle B A C is equal to angle EDF . Q. E. D. EXERCISE . - CASE III . Let the sides given equal be the sides AC and DF , opposite to the equal angles ABC and DEF Required . To prove that- ( a ) BC is ...
... base AC is equal to base DF , and angle B A C is equal to angle EDF . Q. E. D. EXERCISE . - CASE III . Let the sides given equal be the sides AC and DF , opposite to the equal angles ABC and DEF Required . To prove that- ( a ) BC is ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.