First principles of Euclid: an introduction to the study of the first book of Euclid's Elements |
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Σελίδα 7
This is done by assuming as axioms , for the present , Euclid's fourth and eighth propositions . The problems , being much easier than the theorems , and for the most part shorter , at the same time admit of more elaborate treatment ...
This is done by assuming as axioms , for the present , Euclid's fourth and eighth propositions . The problems , being much easier than the theorems , and for the most part shorter , at the same time admit of more elaborate treatment ...
Σελίδα 15
( Not given by Euclid , but assumed by him ) . If the same thing be added to equals the wholes are equal . 3. If equals be taken from equals , the remainders are equal . 3a . ( Not given by Euclid , but assumed by him . ) ...
( Not given by Euclid , but assumed by him ) . If the same thing be added to equals the wholes are equal . 3. If equals be taken from equals , the remainders are equal . 3a . ( Not given by Euclid , but assumed by him . ) ...
Σελίδα 16
( Not given by Euclid , but assumed by him ) . Lines and angles which are equal to one another , coincide with one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II .
( Not given by Euclid , but assumed by him ) . Lines and angles which are equal to one another , coincide with one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II .
Σελίδα 17
When lines coincide their points coincide ( assumed as an axiom ) . A B and CD coincide ( 1st conclusion ( a ) become a premiss ) . ( b ) .. The points of A B and CD coincide ( 2nd conclusion ) . 3rd Syllogism .
When lines coincide their points coincide ( assumed as an axiom ) . A B and CD coincide ( 1st conclusion ( a ) become a premiss ) . ( b ) .. The points of A B and CD coincide ( 2nd conclusion ) . 3rd Syllogism .
Σελίδα 29
... and have also their bases equal ; then the angle contained by the two sides of one triangle shall be equal to the angle contained by the two sides of the other.1 ( Assumed here as an axiom proved on page 76. ) General Enunciation .
... and have also their bases equal ; then the angle contained by the two sides of one triangle shall be equal to the angle contained by the two sides of the other.1 ( Assumed here as an axiom proved on page 76. ) General Enunciation .
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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 |