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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Αποτελέσματα 1 - 5 από τα 79.
Σελίδα 4
... lines CA and CB to the ex- ( 2 ) Post . 1. tremities of the given right line ( 2 ) . It is evident that ACB is a triangle constructed upon the given line ; but it is also equilateral : for the right line AC is equal to AB , as they are ...
... lines CA and CB to the ex- ( 2 ) Post . 1. tremities of the given right line ( 2 ) . It is evident that ACB is a triangle constructed upon the given line ; but it is also equilateral : for the right line AC is equal to AB , as they are ...
Σελίδα 5
... given point A a right line AL has been drawn , equal to the given right line BC . Schol . The position of the right line AL varies ac- cording to the extremity of the given right line from which it is drawn , and also according to the side ...
... given point A a right line AL has been drawn , equal to the given right line BC . Schol . The position of the right line AL varies ac- cording to the extremity of the given right line from which it is drawn , and also according to the side ...
Σελίδα 8
... line cannot have their conterminous sides equal , when the vertex of each of ... line cannot have their conterminous sides equal , if the vertex of one of them be within the other . Thirdly . Let the vertex D ... a given ELEMENTS OF EUCLID ,
... line cannot have their conterminous sides equal , when the vertex of each of ... line cannot have their conterminous sides equal , if the vertex of one of them be within the other . Thirdly . Let the vertex D ... a given ELEMENTS OF EUCLID ,
Σελίδα 9
... A. The right line , joining the points A and F , bisects the given angle BAC . Because the sides AD and AE are equal ( 3 ) , and the ( 3 ) Constr . side AF is common to the triangles FAD and FAE , and the base FD is also equal to FE ( 3 ) ...
... A. The right line , joining the points A and F , bisects the given angle BAC . Because the sides AD and AE are equal ( 3 ) , and the ( 3 ) Constr . side AF is common to the triangles FAD and FAE , and the base FD is also equal to FE ( 3 ) ...
Σελίδα 10
... 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 .么 PROP . XII . PROB . To draw a perpendicular to ...
... 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 .么 PROP . XII . PROB . To draw a perpendicular 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.