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The Elements of Euclid: With Many Additional Propositions, & Explanatory ...
Geen voorbeeld beschikbaar - 2018
ABCD 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 given angle given line greater Hypoth Hypotheses intersect isosceles join less line BC lines be drawn magnitude major premiss parallel parallelogram perpendicular predicate premises produced proposition quadratic equation reductio ad absurdum right angles Scholia Scholium second power segment sides AC sides are equal square on AC square on half squares on AB syllogism termed Theorem Theorem.—If a straight triangle ABC twice the rectangle twice the square vertex whole line
Pagina 34 - 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.
Pagina 124 - 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...
Pagina 4 - 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.
Pagina viii - is a word taken at pleasure to serve for a mark which may raise in our mind a thought like to some thought we had before, and which being pronounced to others, may be to them a sign of what thought the speaker had •)• before in his mind.
Pagina 23 - The difference between any two sides of a triangle is less than the third side.
Pagina 121 - 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.
Pagina 99 - ... 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.
Pagina 80 - 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
Pagina 44 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.