Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green |
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Side 20
The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are
equal , not merely if they are equivalent , they will coincide . 2 . The equality
spoken of is equality of the sides and of the angles . Triangles may be equal in
area ...
The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are
equal , not merely if they are equivalent , they will coincide . 2 . The equality
spoken of is equality of the sides and of the angles . Triangles may be equal in
area ...
Side 21
The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are
equal , not merely if they are equivalent , they will coincide . 2. The equality
spoken of is equality of the sides and of the angles . Triangles may be equal in
area ...
The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are
equal , not merely if they are equivalent , they will coincide . 2. The equality
spoken of is equality of the sides and of the angles . Triangles may be equal in
area ...
Side 27
Q . E . D . Sch . - 1 . This corollary should be ranked among the axioms ; for it is
assumed 1 Prop . 4 , that if certain lines placed on one another coineide for any
portion of their length , they must coincide throughout . It is also assumed in Prop
.
Q . E . D . Sch . - 1 . This corollary should be ranked among the axioms ; for it is
assumed 1 Prop . 4 , that if certain lines placed on one another coineide for any
portion of their length , they must coincide throughout . It is also assumed in Prop
.
Side 35
And therefore the A FKG has its three sides , & c . Q . E . F . SCH . - 1 . In P . 22 it
is assumed that the two circles will have at least one point of intersection . 2 . If
two of the given lines were together equal to the third , the circles would touch ...
And therefore the A FKG has its three sides , & c . Q . E . F . SCH . - 1 . In P . 22 it
is assumed that the two circles will have at least one point of intersection . 2 . If
two of the given lines were together equal to the third , the circles would touch ...
Side 42
It has been objected to the twelfth axiom that it is not self - evident , and that it
forms the converse to P . 27 : now , both the assumed axiom and its converse
should be so obvious as not to require demonstration . 2 . “ The Twelfth Aciom
may be ...
It has been objected to the twelfth axiom that it is not self - evident , and that it
forms the converse to P . 27 : now , both the assumed axiom and its converse
should be so obvious as not to require demonstration . 2 . “ The Twelfth Aciom
may be ...
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Vanlige uttrykk og setninger
ABCD added angle equal apply ascertain assumed Axioms base base BC bisected centre circle circumference coincide common Conc construct contained definition demonstration describe diagonal diameter distance divided draw drawn earth's equal Euclid extremity fall feet figure four Geometry given given point greater half height impossible inches inference intersect join length less line BC measure meet miles named object opposite parallel parallelogram perpendicular plane practical principle produced Prop proposition proved reason rectangle rectil rectilineal representative right angles scale sides square straight line suppose surface thing third triangle true truth units Wherefore whole
Populære avsnitt
Side 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 17 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Side 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Side 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 54 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Side 22 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.
Side 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Bibliografisk informasjon
| Tittel | Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green |
| Forfatter | Euclides |
| Redaktør | Henry Green |
| distribuert | 1863 |
| Original fra | Oxford University |
| Digitalisert | 14. nov 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |