First principles of Euclid: an introduction to the study of the first book of Euclid's Elements |
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Σελίδα 48
We now proceed to prove several of Euclid's theorems by one or other of these methods . THEOREM ( Euclid I. 13 ) . Repeat . The difference between a problem and a theorem ; the definition of a right angle ; and Axioms 1 and 2a .
We now proceed to prove several of Euclid's theorems by one or other of these methods . THEOREM ( Euclid I. 13 ) . Repeat . The difference between a problem and a theorem ; the definition of a right angle ; and Axioms 1 and 2a .
Σελίδα 49
... each of them is a right angle . The line AB standing on the line CD makes the angle ABC equal to the angle A B D. .. Each of the angles ABC , ABD is a right angle . E ( b ) Let us assume that angle A B Theorem ( Euclid I. 13 ) . 49.
... each of them is a right angle . The line AB standing on the line CD makes the angle ABC equal to the angle A B D. .. Each of the angles ABC , ABD is a right angle . E ( b ) Let us assume that angle A B Theorem ( Euclid I. 13 ) . 49.
Σελίδα 51
THEOREM ( Euclid I. 14 ) . Repeat . The enunciation of Euc . I. 13 and Axioms 3a and 11 . General Enunciation . If , at a point in a straight line , two other straight lines , on the opposite sides of it , make the adjacent angles ...
THEOREM ( Euclid I. 14 ) . Repeat . The enunciation of Euc . I. 13 and Axioms 3a and 11 . General Enunciation . If , at a point in a straight line , two other straight lines , on the opposite sides of it , make the adjacent angles ...
Σελίδα 53
... it is also absurd to suppose , as we did ( a ) , that the line BE can be in the same straight line with CB . THEOREM ( Euclid I. 16 ) . Repeat . The Theorem ( Euclid I. 14 ) . 53.
... it is also absurd to suppose , as we did ( a ) , that the line BE can be in the same straight line with CB . THEOREM ( Euclid I. 16 ) . Repeat . The Theorem ( Euclid I. 14 ) . 53.
Σελίδα 56
THEOREM ( Euclid I. 16 ) . Repeat . The enunciations of Euc . I. 15 , I. 4 , and Axiom 9 . General Enunciation . If one side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles .
THEOREM ( Euclid I. 16 ) . Repeat . The enunciations of Euc . I. 15 , I. 4 , and Axiom 9 . General Enunciation . If one side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles .
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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 |