Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Σελίδα 12
... centre of attraction . . The geometrical analysis is a mode of demonstration the very reverse of the synthetic , which is commonly employed in teaching the elements of the science . The former is the method in which researches for the ...
... centre of attraction . . The geometrical analysis is a mode of demonstration the very reverse of the synthetic , which is commonly employed in teaching the elements of the science . The former is the method in which researches for the ...
Σελίδα 26
... centre . " Here the magnitudes can only assume two states , the circles must either have the same centre or they must not , and Euclid proves that the circles cannot have the same centre , and therefore infers that the centres must be ...
... centre . " Here the magnitudes can only assume two states , the circles must either have the same centre or they must not , and Euclid proves that the circles cannot have the same centre , and therefore infers that the centres must be ...
Σελίδα 32
... CENTRE of the circle , the describing line the RADIANT , and the boundary traced by the remote end of the line the CIRCUMFERENCE . 34. The RADIUS of a circle is a straight line drawn from the centre to the circumference . Cor . Hence ...
... CENTRE of the circle , the describing line the RADIANT , and the boundary traced by the remote end of the line the CIRCUMFERENCE . 34. The RADIUS of a circle is a straight line drawn from the centre to the circumference . Cor . Hence ...
Σελίδα 33
... centre , and terminated both ways by the circumference . 36. An ARC of a circle is any part of the circumference . 37. Magnitudes which coincide the whole of one with the whole of the other , or exactly fill the same space , are said to ...
... centre , and terminated both ways by the circumference . 36. An ARC of a circle is any part of the circumference . 37. Magnitudes which coincide the whole of one with the whole of the other , or exactly fill the same space , are said to ...
Σελίδα 34
... centre , with a radiant equal to any given straight line . AXIOMS . 1. Things which are equal to the same thing , or to equal things , are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be ...
... centre , with a radiant equal to any given straight line . AXIOMS . 1. Things which are equal to the same thing , or to equal things , are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2008 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal ABC and DEF ABC is equal acute adjacent angles ancient geometers angle ACD angle AGH angle BAC angles ABC angles equal angular magnitude base BC bisect centre circumference coincide diagonal drawn EBCF equal alternate angles equal Def equal to BC Euclid EUCLID'S ELEMENTS exterior angle figure has sides four right angles geometers given point given straight line greater than AC included angle interior opposite angle intersect isosceles triangle join less Let ABC Let the straight method method of exhaustions parallel lines parallel to CD parallelogram ABCD perpendicular PLANE GEOMETRY point F PROB proof properties of parallel PROPOSITION Pythagoras radius rectangle rectilineal figure reductio ad absurdum Scholium side AB side AC straight line BC THEOR theorem three angles three sides triangle ABC triangle DEF triangles are equal truths unequal vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 43 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Σελίδα 46 - Any two angles of a triangle are together less than two right angles.
Σελίδα 37 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Σελίδα 57 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Σελίδα 38 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.
Σελίδα 68 - 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 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Σελίδα 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Σελίδα 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.