Chap. 2.
Algebraic\ Integers.
3ok l.
samples,: a Debtwill finds Pound,Likewiseds, andoff one\ which
V.
but havefirmative
Se 8 . IV.
)Ught.
- 5a beof — 3 a
-4, that
1 I
Again,
To be added,The Summ,
4~ ab— acad
~b ab — ac -f- ad |
$ddd— 3 dd
'— 4 ^ _
-4- 5 ddd — 3— qd
Addition of Compound Algebraical integers.
VIII. The Addition of Compound whole Quantities may easily be dispatcht by the ofexAr. 9help of the Rules in the preceding Sections of this Chap. as will appeat by the followingExamples. . * . „ \ .
First then’ If this Compound quantity a~\-* b be to be added to a-P"ib, their sumis a 4- b -f- a -j- a b , that is 2 a -+- 3 b ; for a +• a makes z a, and -4- b 2 b makes 3 »•
Again, The Summ of these two Compound quantities 3 b-f-%* am V3^~*~ 54-4-26 — 2a, that is, 56-t- %a- y for 36-j- *b makes 5b j and ( by Sett. V .)
~b 5a — 24 makes 4-3<*• ..
Likewise, The Sumra of these two Compound quantities 5 f *-b 3/—- ® aD “ 3*f ""T2/-v- 6 will be found 8ee-f-/—2: For ;ee added to 3 ee makes 8ee; also 3; addedto — 2/ gives-4-/, and — 8 added to -4-6 makes—a.
After the same manner, 34 — 8 added to 10 — a makes 3 a-4 -a ; (for -4- 3 ^added to —a makes -4- 2 a, and — 8 added to -j-10 gives -b?.)
Again, The Summ of these two Compound quantities a-r-b and c—d is a-rb-f c-a,
Which Summ admits of no Contraction, in regard all the Simple quantities are unlike.
More Examples of the Addition of Compound whole Quantities.
, To be added, £ *+ *
— 3
aa 4 - 4 —- 6
The Summ, 2 a
2 44 4~ 3 4—9
To be added, $ «* — *«[
4 aa-\- ab
«i-bz— 4 c 4 “ id — 2
The Summ, 2 aa — ab
^ -4- I
To be added. $ lee-f 3 ef-ff 1 abc ^6
4 — 3 fe *b• 5ff | -4- $abc — 6
The Summ, — ee 4 - 8 ef-ff J -t- 2 abc
itethem Tst . .. . S — aaa~\~2bba
4bct0 To be added, A 8 aaa^~ A bba
( £ 6444 — 6 bba
44— 54 -4- 24
44 4— A -17
— 244 -j- ia-\- 12
•b^rc, The Summ, \ 3 aaa
— 24-1-59
To be added,
The Sun®,
C a 4~ bA c — d
I - 4 -/ __
a-\- b-\- c — d-\-e -J-/ |
5 ^ 4-242 A 5 4- 4°
— 64
9h\ or, 9 hhh
To
B 2
t H A Pi