Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements |
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Seite 15
Euclid's method of treating of proportion is therefore not well adapted to the purposes of education , and the greater number of students find it necessary to draw their notions of proportion from other sources which , although they may ...
Euclid's method of treating of proportion is therefore not well adapted to the purposes of education , and the greater number of students find it necessary to draw their notions of proportion from other sources which , although they may ...
Seite 20
A line might be drawn from the vertex of any triangle to the base , and by a very simple application of this principle the vertex of the triangle might be conceived to move along this line , gradually changing the form of the triangle ...
A line might be drawn from the vertex of any triangle to the base , and by a very simple application of this principle the vertex of the triangle might be conceived to move along this line , gradually changing the form of the triangle ...
Seite 22
The first of these exceptions is that of a straight line , which is defined by that property which distinguishes it from all other kinds of lines whatsoever , that only one straight line can be drawn from one point to another , and is ...
The first of these exceptions is that of a straight line , which is defined by that property which distinguishes it from all other kinds of lines whatsoever , that only one straight line can be drawn from one point to another , and is ...
Seite 27
... and the argument in support of it has a logical form ; but the mind of the student cannot perceive how such a conclusion can be drawn from the proof adduced , which tends rather to perplex him than to command his rational assent .
... and the argument in support of it has a logical form ; but the mind of the student cannot perceive how such a conclusion can be drawn from the proof adduced , which tends rather to perplex him than to command his rational assent .
Seite 30
When one line only of the same kind can be drawn from one point to another it is called a STRAIGHT LINE . Cor . 1. Hence two straight lines can neither enclose a space nor have a common segment ; for if a second straight line were drawn ...
When one line only of the same kind can be drawn from one point to another it is called a STRAIGHT LINE . Cor . 1. Hence two straight lines can neither enclose a space nor have a common segment ; for if a second straight line were drawn ...
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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
Beliebte Passagen
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.