Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements |
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Seite 46
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the ...
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the ...
Seite 47
The greater side of every triangle has the greater angle opposite to it . ... and because ADB is the exterior angle of the triangle BDC , it is greater ( 16 ) than the interior opposite angle B BCD ; but ADB is equal ABD , because the ...
The greater side of every triangle has the greater angle opposite to it . ... and because ADB is the exterior angle of the triangle BDC , it is greater ( 16 ) than the interior opposite angle B BCD ; but ADB is equal ABD , because the ...
Seite 49
Again , because the exterior angle of a triangle is ( 16 ) greater than the interior opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is ...
Again , because the exterior angle of a triangle is ( 16 ) greater than the interior opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is ...
Seite 51
opposite to the AF E D G less angle , therefore CD is less than CE . Again , CE is less than CF ; for CEF being the exterior angle of the triangle CED , is greater than the interior opposite angle CDE ...
opposite to the AF E D G less angle , therefore CD is less than CE . Again , CE is less than CF ; for CEF being the exterior angle of the triangle CED , is greater than the interior opposite angle CDE ...
Seite 56
A If one side of a triangle be produced , the exterior angle is equal to the two interior opposite angles . Let BC , one of the sides of the triangle ABC , be produced to D , the exterior angle ACD is equal to the interior opposite ...
A If one side of a triangle be produced , the exterior angle is equal to the two interior opposite angles . Let BC , one of the sides of the triangle ABC , be produced to D , the exterior angle ACD is equal to the interior opposite ...
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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Keine Leseprobe verfügbar - 2008 |
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ABC is equal AC is equal acute adjacent alternate angles ancient angle ACD angle BAC angles ABC appears application assume axiom base BC bisect called centre circle circumference coincide common conclusion construction definition demonstration describe determined diagonal draw drawn elements employed established Euclid extended exterior angle extremities fall four right angles geometers geometry given straight line greater half Hence included angle interior opposite angle intersect introduced join knowledge less Let ABC magnitudes manner means meet method mind mode necessary obtuse parallel lines parallelogram perpendicular plane position principle problem produced proof properties PROPOSITION proved radiant reason rectangle rectilineal figure remaining respects side AB side AC surfaces THEOR thing third triangle ABC triangles are equal truths unequal vertex wherefore whole
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Seite 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.
Seite 46 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Seite 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Seite 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.