Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Αποτελέσματα 1 - 5 από τα 9.
Σελίδα 30
... Hence two straight lines can neither enclose a space nor have a common segment ; for if a second straight line were drawn between the same points , it must coincide in every part and become one with the first . Cor . 2. A straight line ...
... Hence two straight lines can neither enclose a space nor have a common segment ; for if a second straight line were drawn between the same points , it must coincide in every part and become one with the first . Cor . 2. A straight line ...
Σελίδα 32
... drawn from the centre to the circumference . Cor . Hence all the radii of the same circle are equal , for each of them is equal to the radiant . 35. The DIAMETER of a circle is a straight line 32 ELEMENTS OF PLANE GEOMETRY .
... drawn from the centre to the circumference . Cor . Hence all the radii of the same circle are equal , for each of them is equal to the radiant . 35. The DIAMETER of a circle is a straight line 32 ELEMENTS OF PLANE GEOMETRY .
Σελίδα 39
... Hence also all the simple angles made by any number of straight lines meeting in one point are together equal to four right angles . PROPOSITION VIII . THEOR . Any two sides of a triangle are together greater than the third side . Let ...
... Hence also all the simple angles made by any number of straight lines meeting in one point are together equal to four right angles . PROPOSITION VIII . THEOR . Any two sides of a triangle are together greater than the third side . Let ...
Σελίδα 45
... hence ( 12 ) the triangles are equal , and therefore the angle B is equal to the angle C. B Ꭰ Cor . 1. Hence every equilateral triangle is also equiangular . Cor . 2. The straight line bisecting the vertical angle of an isosceles ...
... hence ( 12 ) the triangles are equal , and therefore the angle B is equal to the angle C. B Ꭰ Cor . 1. Hence every equilateral triangle is also equiangular . Cor . 2. The straight line bisecting the vertical angle of an isosceles ...
Σελίδα 47
... Hence the less angle of every triangle is opposite to the less side . PROPOSITION XIX . THEOR . If two angles of a triangle are equal , the sides opposite to them are also equal . Let ABC be a triangle having the angle B equal to the ...
... Hence the less angle of every triangle is opposite to the less side . PROPOSITION XIX . THEOR . If two angles of a triangle are equal , the sides opposite to them are also equal . Let ABC be a triangle having the angle B equal to the ...
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.