Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green |
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Resultat 1-5 av 5
Side 25
C . 1 Assum . Take any point D in AB ; 2 by P . 3 & Pst . 1 on AC ' make AE = AD ,
and join DE , 3 P . 1 & Pst . 11 and on DE construct an equil . A , DFE , and join
AF ; 4 Sol . then BAF shall = _ CAF , the BAC being bisected . D . I by C . 2 & P . 1
.
C . 1 Assum . Take any point D in AB ; 2 by P . 3 & Pst . 1 on AC ' make AE = AD ,
and join DE , 3 P . 1 & Pst . 11 and on DE construct an equil . A , DFE , and join
AF ; 4 Sol . then BAF shall = _ CAF , the BAC being bisected . D . I by C . 2 & P . 1
.
Side 31
Make CE = AE , and join BE ; 2 Pst . 2 , P . 3 , 1 produce BE to ? F , Pst . 1 . so that
BE = EF , and join FC . D . 1 by C . 1 & 2 , In AS ABE , CEF . AE = EC , and BE =
EF , 21 P . 15 . and L AEB = Z CEF ; 3 P 4 . 1 . 1 . 4 AEB = A CEF , and BAE FCE .
Make CE = AE , and join BE ; 2 Pst . 2 , P . 3 , 1 produce BE to ? F , Pst . 1 . so that
BE = EF , and join FC . D . 1 by C . 1 & 2 , In AS ABE , CEF . AE = EC , and BE =
EF , 21 P . 15 . and L AEB = Z CEF ; 3 P 4 . 1 . 1 . 4 AEB = A CEF , and BAE FCE .
Side 33
From B draw BD perp . to DG , and produce BDindefinitely ; 2 P . 3 . make DC =
DB , D and join E , C . 3 ) Assum . , Pst . 1 . | Also in DG assume another point F ,
& join CV AF , BF , and CF . D . 1 by C . 1 , 2 . In triangles BED , CED , DE is ...
From B draw BD perp . to DG , and produce BDindefinitely ; 2 P . 3 . make DC =
DB , D and join E , C . 3 ) Assum . , Pst . 1 . | Also in DG assume another point F ,
& join CV AF , BF , and CF . D . 1 by C . 1 , 2 . In triangles BED , CED , DE is ...
Side 46
... it will be found that CD measures 400 feet or yards , according to the unit of
length in AB . PROP . 33 . - THEOR . The st . lines which join the extremities of
two equal and parallel st . lines towards the same parts , are also equal and
parallel .
... it will be found that CD measures 400 feet or yards , according to the unit of
length in AB . PROP . 33 . - THEOR . The st . lines which join the extremities of
two equal and parallel st . lines towards the same parts , are also equal and
parallel .
Side 52
Let the ASABC , DBC , be equal , A and on the same base BC , and on the same
side of it , 2 Conc . then the line joining A and D shall be to BC . C . Il by Pst . 1 .
Join A and D , then AD is BC ; 2 Sup . but suppose them not to be ll , 3 P . 31 , Pst
...
Let the ASABC , DBC , be equal , A and on the same base BC , and on the same
side of it , 2 Conc . then the line joining A and D shall be to BC . C . Il by Pst . 1 .
Join A and D , then AD is BC ; 2 Sup . but suppose them not to be ll , 3 P . 31 , Pst
...
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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 |