First principles of Euclid: an introduction to the study of the first book of Euclid's Elements |
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Σελίδα 35
another it forms two angles . In the figures given here they are the angles CD A , C D B , Now those angles must be either equal or unequal . In fig . 1 they are equal . In fig . 2 they are unequal . .. In fig . I they are right angles ...
another it forms two angles . In the figures given here they are the angles CD A , C D B , Now those angles must be either equal or unequal . In fig . 1 they are equal . In fig . 2 they are unequal . .. In fig . I they are right angles ...
Σελίδα 36
To draw from the point Ca straight line at right angles to AB . A Construction . ( a ) In A C take any point D. ( b ) From CB cut off a part CE equal to CD . ( Euc . I. 3. ) -B Ε D ( c ) On DE describe the equilateral triangle DFE .
To draw from the point Ca straight line at right angles to AB . A Construction . ( a ) In A C take any point D. ( b ) From CB cut off a part CE equal to CD . ( Euc . I. 3. ) -B Ε D ( c ) On DE describe the equilateral triangle DFE .
Σελίδα 38
At the point in the given straight line NO draw a straight line at right angles to NO ( produce NO towards N ) . N III . ... C B Take any point D on the side of A B remote from C. At the centre C and distance CD describe the circle FDG ...
At the point in the given straight line NO draw a straight line at right angles to NO ( produce NO towards N ) . N III . ... C B Take any point D on the side of A B remote from C. At the centre C and distance CD describe the circle FDG ...
Σελίδα 41
I. 8 ( page 46 ) . General Enunciation . C At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle . P E Construction . In CD , CE take any C points Problem ( Euclid I. 23 ) . 41.
I. 8 ( page 46 ) . General Enunciation . C At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle . P E Construction . In CD , CE take any C points Problem ( Euclid I. 23 ) . 41.
Σελίδα 42
In CD , CE take any C points D and E. Join DE . By means of Euc . I. 22 construct the triangle AFG , ( a ) having its side AF equal to CD ; its side A G equal to CE ; and its side FG equal to DE . Then the angle FAG shall be equal to ...
In CD , CE take any C points D and E. Join DE . By means of Euc . I. 22 construct the triangle AFG , ( a ) having its side AF equal to CD ; its side A G equal to CE ; and its side FG equal to DE . Then the angle FAG shall be equal to ...
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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 |