Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Resultat 1-5 av 24
Side 38
... AB , let the two straight lines BC and BD , on the opposite sides of AB , make the adjacent angles ABC and ABD together equal to two right angles , BD is in the same straight line with BC . For if BD be not in the same straight line ...
... AB , let the two straight lines BC and BD , on the opposite sides of AB , make the adjacent angles ABC and ABD together equal to two right angles , BD is in the same straight line with BC . For if BD be not in the same straight line ...
Side 39
... AB and CD cut one another in the point E , the angle AEC is equal to DEB , and the angle CEB to AED . E B D For the ... Let ABC be a triangle , any two of its sides are together greater than the third . A For as a straight line is ( Def ...
... AB and CD cut one another in the point E , the angle AEC is equal to DEB , and the angle CEB to AED . E B D For the ... Let ABC be a triangle , any two of its sides are together greater than the third . A For as a straight line is ( Def ...
Side 42
... Let ABC and DEF be two triangles which have the side AB equal to DE , AC to DF , and BC to EF , the triangles are equal ( Def . 37 ) . For if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and 42 ...
... Let ABC and DEF be two triangles which have the side AB equal to DE , AC to DF , and BC to EF , the triangles are equal ( Def . 37 ) . For if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and 42 ...
Side 43
... Let the two triangles ABC and EDF have the side AB equal to DE , AC to DF , and the included angle A equal to D , the base BC shall be equal to the base EF , and the triangles shall be every way equal . For if the triangle ABC be ...
... Let the two triangles ABC and EDF have the side AB equal to DE , AC to DF , and the included angle A equal to D , the base BC shall be equal to the base EF , and the triangles shall be every way equal . For if the triangle ABC be ...
Side 44
... ABC and DEF have equal boundaries , and coincide in three points not in the ... Let BAC be a given rectilineal angle , it is required to bisect it , that is ... ABC , let the side AB be 44 ELEMENTS OF PLANE GEOMETRY . to DE; and AC shall ...
... ABC and DEF have equal boundaries , and coincide in three points not in the ... Let BAC be a given rectilineal angle , it is required to bisect it , that is ... ABC , let the side AB be 44 ELEMENTS OF PLANE GEOMETRY . to DE; and AC shall ...
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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Ingen forhåndsvisning tilgjengelig - 2008 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 46 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Side 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Side 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.