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 2
... perpendicular to it . 12. The angle ( ABC ) , which is greater than a right angle , is called obtuse . 13. The angle ( ABD ) , which is less than a right angle , is called acute . 14. A plane figure is a plane surface , which is bound ...
... perpendicular to it . 12. The angle ( ABC ) , which is greater than a right angle , is called obtuse . 13. The angle ( ABD ) , which is less than a right angle , is called acute . 14. A plane figure is a plane surface , which is bound ...
Σελίδα 9
... perpendicular to the given line . In the given line take any point D , and make CE equal to CD ( 1 ) ; upon DE describe an equilateral tri- ( 1 ) Prop . 3 . angle DFE ( 2 ) , draw FC , and it is perpendicular to the ( 2 ) Prop . 1 ...
... perpendicular to the given line . In the given line take any point D , and make CE equal to CD ( 1 ) ; upon DE describe an equilateral tri- ( 1 ) Prop . 3 . angle DFE ( 2 ) , draw FC , and it is perpendicular to the ( 2 ) Prop . 1 ...
Σελίδα 10
... perpendicular to the given right ( 5 ) Def . 11. line AB at the point Ĉ ( 5 ) . ( 4 ) Schol . Fig . 25 . See N. Schol . In the same manner a perpendicular can be erected at the extremity of a given line , by first pro- ducing the line ...
... perpendicular to the given right ( 5 ) Def . 11. line AB at the point Ĉ ( 5 ) . ( 4 ) Schol . Fig . 25 . See N. Schol . In the same manner a perpendicular can be erected at the extremity of a given line , by first pro- ducing the line ...
Σελίδα 12
... perpendicular to it , the other not ; the perpendicular falls at the side of the acute angle . For , if possible , let BA perpendicular to the line ED fall at the side of the obtuse angle BCE , then the ( 1 ) Def . 12. angle BAE is less ...
... perpendicular to it , the other not ; the perpendicular falls at the side of the acute angle . For , if possible , let BA perpendicular to the line ED fall at the side of the obtuse angle BCE , then the ( 1 ) Def . 12. angle BAE is less ...
Σελίδα 14
... perpendicular to ED , the other not ; BC is less than BA . For in the triangle ABC the angle BAC is acute , since BCA is right ( 1 ) ; therefore BC is opposite to the less angle , and therefore is less than BA , which is op- posite to ...
... perpendicular to ED , the other not ; BC is less than BA . For in the triangle ABC the angle BAC is acute , since BCA is right ( 1 ) ; therefore BC is opposite to the less angle , and therefore is less than BA , which is op- posite to ...
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.