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 23.
Σελίδα 20
AE is equal to C. ( Axiom I. ) Wherefore from AB , the greater of two given straight lines , a part A E , has been cut off equal to C the less . Q. E. F. EXERCISE . - Write out the whole of this problem , using the contracted syllogisms ...
AE is equal to C. ( Axiom I. ) Wherefore from AB , the greater of two given straight lines , a part A E , has been cut off equal to C the less . Q. E. F. EXERCISE . - Write out the whole of this problem , using the contracted syllogisms ...
Σελίδα 28
If the line AC fall within the angle ED F , the angle B A C is less than EDF . But if the line A C fall without the angle E D F , then the angle B A C is greater than E D F. Try this with cardboard angles of various sizes .
If the line AC fall within the angle ED F , the angle B A C is less than EDF . But if the line A C fall without the angle E D F , then the angle B A C is greater than E D F. Try this with cardboard angles of various sizes .
Σελίδα 59
Any two angles of a triangle are together less than two right angles . Particular Enunciation . Given . The triangle B. ABC . A Required . To prove that any two of its angles Theorem ( Euclid I. 17 ) . 59 II 13 15 16.
Any two angles of a triangle are together less than two right angles . Particular Enunciation . Given . The triangle B. ABC . A Required . To prove that any two of its angles Theorem ( Euclid I. 17 ) . 59 II 13 15 16.
Σελίδα 60
To prove that any two of its angles taken together are less than two right angles . Construction . We will prove that angles A B C and A CB , are together less than two right angles . Produce the side B C to D. B Proof ( by Euc .
To prove that any two of its angles taken together are less than two right angles . Construction . We will prove that angles A B C and A CB , are together less than two right angles . Produce the side B C to D. B Proof ( by Euc .
Σελίδα 61
ABC and B A C are together less than two right angles . III . Prove that angles A B C , and ACB in this figure are together less than two right angles , without producing either side . ( Notice that A B D A A B and ACD are two triangles ...
ABC and B A C are together less than two right angles . III . Prove that angles A B C , and ACB in this figure are together less than two right angles , without producing either side . ( Notice that A B D A A B and ACD are two triangles ...
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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 |