The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
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Side 11
Then ( 1 ) shall the base BC be equal to the base EF ; and ( 2 ) the triangle ABC
to the triangle DEF ; and ( 3 ) the other angles to which the equal sides are
opposite shall be equal , each to each — viz . , the angle ABC to the angle DEF ,
and ...
Then ( 1 ) shall the base BC be equal to the base EF ; and ( 2 ) the triangle ABC
to the triangle DEF ; and ( 3 ) the other angles to which the equal sides are
opposite shall be equal , each to each — viz . , the angle ABC to the angle DEF ,
and ...
Side 13
the two sides FA , AC are equal to the two GA , AB , each to each , and they
contain the angle FĀG common to the two triangles AFC , AGB ; therefore 1. The
base FC is equal to ... to which the equal sides are opposite , viz.2. The angle
ACF is ...
the two sides FA , AC are equal to the two GA , AB , each to each , and they
contain the angle FĀG common to the two triangles AFC , AGB ; therefore 1. The
base FC is equal to ... to which the equal sides are opposite , viz.2. The angle
ACF is ...
Side 14
And since it has been demonstrated , that the whole angle ABG is с F E equal to
the whole ACF , the parts of which , the ... If two angles of a triangle be equal to
each other , the sides also which subtend , or are opposite to , the equal angles ...
And since it has been demonstrated , that the whole angle ABG is с F E equal to
the whole ACF , the parts of which , the ... If two angles of a triangle be equal to
each other , the sides also which subtend , or are opposite to , the equal angles ...
Side 24
PROPOSITION 14. - Theorem . If at a point in a straight line , two other straight
lines upon the opposite sides of it , make the adjacent angles together equal to
two right angles , then these two straight lines shall be in one and the same
straight ...
PROPOSITION 14. - Theorem . If at a point in a straight line , two other straight
lines upon the opposite sides of it , make the adjacent angles together equal to
two right angles , then these two straight lines shall be in one and the same
straight ...
Side 25
If two straight lines cut one another , the vertical , or opposite angles shall be
equal . Let the two straight lines AB , CD cut one another in the point E. Then the
angle AEC shall be equal to the angle DEB , and the angle CEB to the angle
AED .
If two straight lines cut one another , the vertical , or opposite angles shall be
equal . Let the two straight lines AB , CD cut one another in the point E. Then the
angle AEC shall be equal to the angle DEB , and the angle CEB to the angle
AED .
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD AC is equal alternate angle ABC angle ACB angle BAC base base BC bisected centre circle ABC circumference common compounded constr Construction contained Demonstration describe diameter divided double draw equal angles equiangular equimultiples exterior angle extremities fall figure four fourth given point given straight line greater half inscribed interior join less Let ABC likewise magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular plane polygon Problem produced proportionals proved Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square on AC taken third touches the circle triangle ABC unequal wherefore whole
Populære avsnitt
Side 4 - 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 230 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Side 110 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 207 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Side 267 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 197 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 21 - 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 61 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Side 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Bibliografisk informasjon
| Tittel | The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
| Forfatter | Euclides |
| Redaktør | James Martin (of the Wedgwood inst, Burslem) |
| distribuert | 1874 |
| Original fra | Oxford University |
| Digitalisert | 8. sep 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |