First principles of Euclid: an introduction to the study of the first book of Euclid's Elements |
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Αποτελέσματα 6 - 10 από τα 11.
Σελίδα 77
... DEF , GEF , having the two sides DE , GE equal , and also the two sides DF , G F equal . But this is impossible ( Euc . I. 7 ) . ... BA , AC must coincide with ED , D F. and ... the angle BAC coincides with the angle E D F ...
... DEF , GEF , having the two sides DE , GE equal , and also the two sides DF , G F equal . But this is impossible ( Euc . I. 7 ) . ... BA , AC must coincide with ED , D F. and ... the angle BAC coincides with the angle E D F ...
Σελίδα 79
If two triangles have two sides of the one equal to two sides of the other , each to each , but the angle contained by the two sides of the one , greater than the angle contained by the ... ( c ) The angle BAC greater than the angle EDF .
If two triangles have two sides of the one equal to two sides of the other , each to each , but the angle contained by the two sides of the one , greater than the angle contained by the ... ( c ) The angle BAC greater than the angle EDF .
Σελίδα 82
To prove that— The angle contained by the two sides of the triangle with the greater base , is greater than the ... The angle BAC must be either 1. equal to angle EDF , or II . less than angle EDF , or III . greater than angle EDF . 1.
To prove that— The angle contained by the two sides of the triangle with the greater base , is greater than the ... The angle BAC must be either 1. equal to angle EDF , or II . less than angle EDF , or III . greater than angle EDF . 1.
Σελίδα 85
CASE I. Let the two sides given equal , ( d ) be the sides BC and EF , adjacent to the equal angles . Required . To prove that— ( e ) AB is equal to DE , ( f ) AC is equal to D F , ( g ) angle BAC is equal to angle EDF . Proof .
CASE I. Let the two sides given equal , ( d ) be the sides BC and EF , adjacent to the equal angles . Required . To prove that— ( e ) AB is equal to DE , ( f ) AC is equal to D F , ( g ) angle BAC is equal to angle EDF . Proof .
Σελίδα 86
I. 4 ) the base AC is equal to the base D F , and the remaining angle BAC is equal to the remaining angle EDF . Q. E. D. CASE II . Let the sides given equal be the ( d ) sides A B and DE , opposite to the equal angles A CB and DFE ( see ...
I. 4 ) the base AC is equal to the base D F , and the remaining angle BAC is equal to the remaining angle EDF . Q. E. D. CASE II . Let the sides given equal be the ( d ) sides A B and DE , opposite to the equal angles A CB and DFE ( see ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD angle A CD angle ABC angle B A C angle BAC angle contained angle EDF angles BGH angles equal assumed Axiom Axiom 2a base base B C bisected called centre circle circumference coincide Construction definition describe diameter double draw enunciations of Euc equal angles equal to angle equilateral triangle EXERCISE EXERCISES.-I exterior angle fall figure given point given straight line greater than angle Hence included angle interior opposite angle Join less Let us suppose letters line A B line AB line CD major premiss meet parallel parallelogram Particular Enunciation perpendicular produced Proof proposition prove that angle Repeat Required right angles side A C sides equal square standing Syllogism THEOREM Euclid thing third triangle ABC unequal
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Πληροφορίες βιβλιογραφίας
| Τίτλος | First principles of Euclid: an introduction to the study of the first book of Euclid's Elements |
| Συγγραφέας | T S. Taylor |
| Εκδόθηκε | 1880 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 7 Σεπτ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |