The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Μέρος 1John Weale, 1853 - 136 σελίδες |
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Σελίδα 3
... scholia . 9. A RIGHT ANGLE is half the angle , formed by a straight line with its continuation . SCHOLIUM . The line which divides the angle formed by a straight line with its continuation , into two right angles , is said to be ...
... scholia . 9. A RIGHT ANGLE is half the angle , formed by a straight line with its continuation . SCHOLIUM . The line which divides the angle formed by a straight line with its continuation , into two right angles , is said to be ...
Σελίδα 10
... SCHOLIA . 1. The construction of this problem will somewhat vary according to the relative posi- tions of the point A and the line BC . ( e ) Def . 13 and 16 . Construction . ( g ) Ax . 3 . ( h ) Ax . 1 . 2. In practice this problem ...
... SCHOLIA . 1. The construction of this problem will somewhat vary according to the relative posi- tions of the point A and the line BC . ( e ) Def . 13 and 16 . Construction . ( g ) Ax . 3 . ( h ) Ax . 1 . 2. In practice this problem ...
Σελίδα 11
... SCHOLIA . 1. In the above demonstration ( at b ) an axiom is assumed the converse of the eighth axiom , namely , " Magnitudes which are equal coin- cide with one another when similarly placed . " 2. In every triangle there are six ...
... SCHOLIA . 1. In the above demonstration ( at b ) an axiom is assumed the converse of the eighth axiom , namely , " Magnitudes which are equal coin- cide with one another when similarly placed . " 2. In every triangle there are six ...
Σελίδα 13
... SCHOLIA . 1. This proposition may also be proved in the following manner : if the triangle ABC be turned over on the plane ( see scholium 3 to the preceding pro- position ) , so that the position of the point A may be unaltered , while ...
... SCHOLIA . 1. This proposition may also be proved in the following manner : if the triangle ABC be turned over on the plane ( see scholium 3 to the preceding pro- position ) , so that the position of the point A may be unaltered , while ...
Σελίδα 14
... SCHOLIA . 1. It should be observed that the portion equal to the lesser side must be cut off from that end of AB next to the equal angle ; otherwise no proof can be drawn from proposition iv . 2. This proposition is the converse of the ...
... SCHOLIA . 1. It should be observed that the portion equal to the lesser side must be cut off from that end of AB next to the equal angle ; otherwise no proof can be drawn from proposition iv . 2. This proposition is the converse of the ...
Άλλες εκδόσεις - Προβολή όλων
The elements of Euclid, [books I.-VI. XI. XII.] with many additional ... Eucleides Πλήρης προβολή - 1853 |
The Elements of Euclid with Many Additional Propositions and Explanatory Notes Henry Law,Eucleides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AC and CB AC is equal angle ABC angle BCD angle equal area to double area to twice bisect chord circle ABC circumference Constr CONSTRUCTION COROLLARY DB is equal DEMONSTRATION diagonal divided double the rectangle draw equal angles equal in area equal to AC equilateral Euclid external angle Find the center finite straight line Geometry given angle given line greater Hypoth HYPOTHESES intersect join less line BC lines be drawn magnitude major premiss opposite sides parallel parallelogram perpendicular predicate premises produced proposition quadratic equation reductio ad absurdum right angles SCHOLIA SCHOLIUM second power segment sides AC square on AC square on half squares on AB syllogism termed THEOREM THEOREM.-If triangle ABC twice the rectangle twice the square vertex whole line
Δημοφιλή αποσπάσματα
Σελίδα 24 - 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 114 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Σελίδα xiv - 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 : 16. And this point is called the centre of the circle.
Σελίδα 13 - The difference between any two sides of a triangle is less than the third side.
Σελίδα 111 - AFC. (in. 21.) Hence in the triangles ADE, AFC, there are two angles in the one respectively equal to two angles in the other, consequently, the third angle CAF is equal to the third angle DAB ; therefore the arc DB is equal to the arc CF, (in.
Σελίδα 89 - ... the centre of the circle shall be in that line. Let the straight line DE touch the circle ABC in C, and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA.
Σελίδα 70 - EQUAL circles are those of which the diameters are equal, or from the centres of which the straight lines to the circumferences are equal. ' This is not a definition, but a theorem, the truth of ' which is evident; for, if the circles be applied to one ' another, so that their centres coincide, the circles ' must likewise coincide, since the straight lines from
Σελίδα 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Σελίδα 22 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...