The First Six Books of the Elements of Euclid: With NotesPrinted at the University Press, for R. Milliken and son, 1833 - 183 σελίδες |
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Σελίδα 52
... that contain the angle . 9. A sector of a circle is the figure contained by two radii and the arch between them . 10. Similar segments of circles are those , which con- tain equal angles . PROP . I. PROB . To find the centre of.
... that contain the angle . 9. A sector of a circle is the figure contained by two radii and the arch between them . 10. Similar segments of circles are those , which con- tain equal angles . PROP . I. PROB . To find the centre of.
Σελίδα 68
... similar segments of circles cannot be constructed which do not coincide . For , if it be possible , let two similar segments ACB and ADB be constructed , and let the point D in one of them fall without the other , and draw the right ...
... similar segments of circles cannot be constructed which do not coincide . For , if it be possible , let two similar segments ACB and ADB be constructed , and let the point D in one of them fall without the other , and draw the right ...
Σελίδα 69
... similar ( 4 ) ; ( 3 ) Prop.20 . but they stand upon equal right lines AC and DF , and et Ax . 7 . are therefore equal ( 5 ) ; take away these equals from the ( 5 ) Prop.24 . ( 4 ) Def . 10 . equal circles , and the remaining segments ...
... similar ( 4 ) ; ( 3 ) Prop.20 . but they stand upon equal right lines AC and DF , and et Ax . 7 . are therefore equal ( 5 ) ; take away these equals from the ( 5 ) Prop.24 . ( 4 ) Def . 10 . equal circles , and the remaining segments ...
Σελίδα 70
... remaining arches ABC and DEF shall be equal ( 4 ) , and therefore the angles AGC and DKF also equal ( 2 ) , and the segments AGC ( 3 ) Prop . 4 . B. 1 . ( 4 ) Ax . 3 . and DKF similar ( 5 ) ; but the lines 70 ELEMENTS OF EUCLID ,
... remaining arches ABC and DEF shall be equal ( 4 ) , and therefore the angles AGC and DKF also equal ( 2 ) , and the segments AGC ( 3 ) Prop . 4 . B. 1 . ( 4 ) Ax . 3 . and DKF similar ( 5 ) ; but the lines 70 ELEMENTS OF EUCLID ,
Σελίδα 71
With Notes Euclid. and DKF similar ( 5 ) ; but the lines AC and DF are ( 5 ) Def . 10 . equal , therefore the segments AGC and DKF are equal ( 6 ) , and therefore the sectors AOC and DHF are ( 6 ) Prop.24 . equal ( 7 ) . ( 7 ) Ax . 2 ...
With Notes Euclid. and DKF similar ( 5 ) ; but the lines AC and DF are ( 5 ) Def . 10 . equal , therefore the segments AGC and DKF are equal ( 6 ) , and therefore the sectors AOC and DHF are ( 6 ) Prop.24 . equal ( 7 ) . ( 7 ) Ax . 2 ...
Συχνά εμφανιζόμενοι όροι και φράσεις
absurd AC and BD AC and CB AC is equal angle ABC angle ACD angle BAC angle equal base bisected centre circumference Constr constructed contained in CD demonstrated described double the rectangle double the square drawn equal angles equal to AC equal to double equi equi-multiples equi-submultiples equiangular Euclid evident external angle fore form one right four magnitudes proportional four right angles fourth given angle given circle given line given right line given triangle gles half a right Hypoth inscribed less line CD manner multiple oftener opposite parallel parallelogram perpendicular PROB produced Prop proposition radius rectangle under AC right angles right line AB Schol segment side AC sides AB similar squares of AC submultiple taken tangent THEOR third tiple triangle ABC vertex
Δημοφιλή αποσπάσματα
Σελίδα 147 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Σελίδα 3 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Σελίδα 22 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 16 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Σελίδα 148 - A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Σελίδα 2 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 92 - F) a ratio compounded of the ratios which the first has to the second, the second to the third, the third to the fourth (A to D, D to C, and C to F) ; and so on to the last.
Σελίδα 93 - AXIOMS. 1. Equimultiples of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes, of which the same or equal magnitudes are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of a less. 4. That magnitude, of which a multiple is greater than the same multiple of another, is greater than that other magnitude.
Σελίδα 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 2 - 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.