a, reducer, connecting the pipe 
of larger diameter t> with the pipe 
of smaller diameter c. 
reducement 
By this we shall know whether yours be that ancient 
Prelaty which you say was first constituted for the reduce- 
ment of quiet and unanimity into the Church. 
Milton, Church-Government, i. 6. 
2. Reduction; abatement. 
After a little reducement of his passion, and that time 
and further meditation had disposed his senses to their 
perfect estate. 
History of Patient Grisel, p. 40. (UaUiu'M.) 
reducent (re-du'sent), a. and n. [< L. redu- 
cen(t-)s, ppr. of reducere : see reduce.} I. a. 
Tending to reduce. 
II. H. That which reduces. Imp. Diet. 
reducer (re-du'ser), n. 1. One who or that 
which reduces, in any sense. 
The last substances enumerated are those in general use 
as reducers or developers in photography. 
Stiver Sunbeam, p. 95. 
An accumulator is indeed merely a chemical converter 
which is unequalled as n pressure-rcdwcer. 
Electric Ren. (Eng.), XXV. 583. 
2. A joint-piece for connecting pipes of vary- 
ing diameter. It may 
be of any form, straight, 
bent, etc. Also called 
reducing-coupling . 
reducibility (re-du-si- 
bil'i-ti), n. [< reducible 
+ -ity (see -bility).~\ 
Eeducibleness ; reduc- 
tibility. 
The theorem of the reducibility of the general problem 
of transformation to the rational is, however, stated with- 
out proof in this paper. Eitcyc. Brit., XIII. 70. 
It was, however, quite evident, from . . . the history 
and the complete reducibility of the tumour, that It must 
be a pulmonary hernia. Lancet, No. S429, p. 1002. 
reducible (re-du'si-bl), a. [< OF. reducible = 
Sp. reducible = Pg. reduzivel = It. riditeibile; as 
reduce + -ible. Of. reduceable.] Capable of be- 
ing reduced; convertible. 
In the new World they have a World of Drinks ; for there 
is no Root, Flower, Fruit, or Pulse but is reducible to a 
notable Liquor. Howell, Letters, ii. 54. 
The line of its motion was neither straight nor yet re- 
ducible to any curve or mixed line that I had met with 
among mathematicians. Boyle, Works, III. 683. 
I have never been the less satisfied that no cause reduci- 
ble to the known laws of nature occasioned my sufferings. 
Barham, Ingoldsby Legends, I. 198. 
Reducible circuit. See circuit. Reducible hernia, 
a hernia whose contents can be returned by pressure or 
posture. 
reducibleness (re-du'si-bl-nes), n. The quality 
of being reducible. 
The reduciMenesa of ice back again into water. 
Boyle, Works, in. 60. 
reducibly (re-du'si-bli), adv. In a reducible 
manner. 
reducine (re-du'sin), n. [< reduce + -ine z .] A 
decomposition product of urpchrome. 
reducing-COUpling ( re - du ' sing -kup" ling), n. 
Same as reducer, 2. 
reducing-press (re-du'sing-pres), n. An aux- 
iliary press used in sheet-metal work to com- 
plete shapes that have been partially struck up. 
reducing-scale (re-du'sing-skal), n. A form of 
scale used by surveyors to reduce chains and 
links to acres and roods by inspection, and also 
in mapping and drawing to different scales ; a 
surveying-scale. 
reducing-T (re-du'sing-te), H. A T-shaped pipe- 
coupling, having arms different from the stem 
in diameter of opening. It is used to unite 
pipes of different sections. Also written redu- 
ciny-ti f. 
reducing-valve (re-du'sing-valv), n. In steam- 
engin., a peculiar 'valve controlled by forces 
acting in opposite directions. The parts are so ar- 
ranged that the valve opens to its extreme limit only when 
the pressure on the delivery side is at a prescribed mini- 
mum, closing the part in the valve-seat more or less when 
this minimum is exceeded. The pressure on the delivery 
side of the valve is thus kept from varying (except between 
very narrow limits) from its predetermined pressure, al- 
though the pressure on the opposite side may be variable, 
and always higher than on the delivery side. Such valves 
are much used for maintaining lower pressures in steam- 
heating and -drying apparatus than is carried in the boiler. 
They are also used in automatic air-brakes for railways 
and in other pneumatic machines, and, in some forms, as 
Kas-regulators for equalizing the pressure of gas delivered 
to gas-burners, etc. Also called pressure-reducing valoe. 
reductt (re-dukf), c. t. [< L. reducing, pp. of 
reducere, lead or bring back: see reduce.'] To 
reduce. 
All the kynges host there beying assembled and reducte 
into one eompanye. Hall, Edw. IV., an. 10. 
Pray let mereduct sometwo or three shillingsfor points 
and ribands. 
B. Jonsoit, Every Man out of his Humour, iv. 5. 
reduct (re-dukf), n. [< ML. reducing, a with- 
drawing-place : see redout 2 .] In building, alit- 
316 
5025 
tie piece or cut taken out of a part, member, 
etc., to make it more uniform, or for any other 
purpose; a quirk, (iieilt. 
reductibility (re-duk-ti-bil'i-ti), n. [= F. re- 
iliirtibilitr; us reduct + -ibiliti/.] The quality 
of being reducible ; reducibleness. Imp. Diet. 
reductio ad abSurdum(re-duk'shi-6 ad ab-ser'- 
dum). [L. : reductio, a leading, reduction ; ad, 
to; absurdum, neut. of absitrdus, absurd: seeofc- 
surd.] A reduction to an absurdity; the proof 
of a proposition by proving the falsity of its 
contradictory opposite : an indirect demonstra- 
tion. In geometry the reductio ad absurdum consists in 
drawing a figure whose parts are supposed to have certain 
relations, and then showing that this leads to a conclusion 
contrary to a known proposition, whence it follows that 
the parts of the figure cannot have those relations. Thus, 
in Euclid's "Elements" the proposition that if a triangle 
has two angles equal the sides opposite those angles will 
be equal is proved as follows. In the triangle ABC, let the 
angles ABC and ACB be equal. Then, suppose AK to be 
greater than AC. Lay off BD = AC and join 
DC. Then, comparing the two triangles ACB 
and 1>BC, we have in the former the sides AC 
and BC and their included angle ACB equal 
iu the latter to the sides DB and CB and their 
included angle DEC. Hence, these two tri- 
angles would be equal, or the part would be 
equal to the whole. This proof is a reductio 
ad absurdum. This kind of reasoning is con- 
sidered somewhat objectionable as not show- 
ing the principle from which the proposi- B 
tion Hows; but it is a perfectly conclusive 
mode of proof, and, in fact, is in all cases readily converted 
into a direct proof. Thus, in the above example, we have 
only to compare the triangle ABC with itself, considering 
it as two triangles according as the angle B is named be- 
fore C or vice versa. In the triangle ABC the angles B and 
C with the included side BC are respectively equal in the 
triangle ACB to the angles C and B with the included Bide 
CB ; hence the other parts of the triangles are equal, and 
the side AC opposite the first angle B in the first triangle 
is equal to the side AB opposite the first angle C in the 
second triangle. 
reduction (re-duk'shon), . [< OF. reduction, 
F. reduction = Pr. reductio = Sp. reduccion = 
Pg. reducqffo = It. ridueione, < L. reductio(n-), 
a leading or bringing back, a restoring, restora- 
tion, < reducere, lead or bring back: see reduce, 
reduct.'] The act of reducing, or the state of 
being reduced, (at) The act of bringing back or re- 
storing. 
For reduction of your majesty's realm of Ireland to the 
unity of the Church. Bp. Burnet, Records, II. ii. 
(6) Conversion into another state or form : as, the reduc- 
tion of a body to powder ; the reduclionot things to order. 
(c) Diminution : as, the reduction of the expenses of gov- 
ernment ; the reduction of the national debt ; a reduc- 
tion of 25 per cent, made to wholesale buyers. 
Let him therefore first make the proper reduction in 
the account, and then see what it amounts to. 
Waterland, Works, VI. 186. 
(d) Conquest ; subjugation : as, the reduction of a prov- 
ince under the power of a foreign nation ; the reduction 
of a fortress. () A settlement or parish of South Amer- 
ican Indians converted and trained by the Jesuits. 
Governing and civilizing the natives of Brazil and Par- 
aguay in the missions and reductions, or ministering, at 
the hourly risk of his life, to his coreligionists in England 
under Elizabeth and James I., the Jesuit appears alike 
devoted, indefatigable, cheerful, and worthy of hearty ad- 
miration and respect. Encyc. Brit., XIII. 649. 
The Indians [under the Jesuits in Paraguay] were gath- 
ered into towns or communal villages called bourgaden 
or reductions, where they were taught the common arts, 
agriculture, and the practice of rearing cattle. 
Johns Hopkins Univ. Studies, 8th ser., IV. 32. 
(/) The bringing of a problem to depend on a problem 
already solved. (17) The transformation of an algebraic 
expression into another of a simpler kind. (A) The low- 
ering of the values of the numerator and denominator of 
a fraction, or of the antecedent and consequent of a ratio, 
by dividing both by the same quantity, (t) The conver- 
sion of a quantity expressed in termsof one denomination 
so as to express it in terms of another denomination. As- 
cending reduction is conversion to terms of larger units ; 
descending reduction, conversion to terms of smaller units. 
( f) The proof of the conclusion of an indirect syllogism 
from its premises by means of a direct syllogism and im- 
mediate inferences. This is said to be a reduction to the 
redundant 
Baroco. 
All M is P. 
Some S is not P. 
Ergo, Some S is not M. 
Reductio per impossibile. 
All M is P. 
All S is it. 
Ergo, All S is P. 
Chasles-Zeuthen reduction, a method of finding how 
many figures fulfil certain conditions, by the considera- 
tion of degenerate figures composed of simpler figures 
with lower constants. Thus, in this way we readily find 
that the number of conies touching five given conies in 
a plane is 3,264. Iron-reduction process. See pro- 
cess. Long reduction, in logic, a reduction in which the 
major premise of the original syllogism becomes the minor 
premise, and vice versa, and in which one of the premises 
and the conclusion are converted. Example: 
Long Reduction. 
No P is S. 
All SI is P. 
Ergo, No M is 8. 
mode of direct syllogism employed. (*) A direct syllogism 
proving, by means of conversions and other immediate 
inferences, that the conclusion of an indirect syllogism 
follows from its premises. (I) The act or process of 
making a copy of a figure, map, design, draft, etc., on a 
smaller scale, preserving the original proportions; also, 
the result of this process, (m) In surg., the operation of 
restoring a dislocated or fractured bone to its former 
place. (71) Separation of a metal from substances com- 
bined with it: used especially with reference to lead, 
zinc, and copper, and also applied to the treatment of iron 
ore, as when steel is made from it by a direct process, 
(o) In astron., the correction of observed quantities for 
instrumental errors, as well as for refraction, parallax, 
aberration, precession, and nutation, so as to bring out 
their cosmical significance. A similar process is applied 
to observations in other physical sciences, (p) In Scots 
law, an action for setting aside a deed, writing, etc. 
Apagogical reduction, in logic, a reduction in which 
the contradictory of the conclusion becomes one of the 
premises, and the contradictory of one of the premises 
the conclusion. Apagogical reduction is an application 
of the reductio ad absurdum, and is also called reductio 
per impossibile. Example: 
Camestres. 
All M is P. 
No S is P. 
Ergo, No S is M. 
Ostensive reduction, that reduction which has for its 
premises the original premises or their conversions, and 
for its conclusion the original conclusion or its converse. 
Reduction and reduction-improbation.in Scots law, 
the designations given to the two varieties of rescissory 
actions. See improbation, 2. Reduction reductive, an 
action in which a decree of reduction which has been erro- 
neously or improperly obtained is sought to be reduced. 
Reduction to the ecliptic, the difference between 
the anomaly of a planet reckoned from its node and the 
longitude reckoned from the same point. Short reduc- 
tion, in logic, a reduction which differs from the original 
syllogism only in having one of its premises converted. 
The following is an example : 
Cesare. Short Reduction. 
No 51 is P. No P is M. 
All S Is P. All S is P. 
Ergo, No S is II. Ergo, No S is M. 
= Syn. (c) Lessening, decrease, abatement, curtailment, 
abridgment, contraction, retrenchment. 
reduction-compasses (re-duk'shon-kurn"pas- 
ez), n. pi. Proportional dividers, or whole-and- 
half dividers. 
reduction-formula (re-duk'shon-f6r"mu-la), n. 
In the integral calculus, a formula depending on 
integration by parts, reducing an integral to 
another nearer to one of the standard forms. 
reduction-works (re-dnk'shpn-werks), n. sing. 
&uApl. A metallurgical establishment ; smelt- 
ing-works. 
reductive (re-duk'tiv), a. and w. [= F. rdduc- 
tif = Sp. Pg'. reductii-o = It. riduttivo, < L. re- 
ductus, pp. of reducere, lead or bring back: see 
reduct, reduce.] I. a. Having the property, 
power, or effect of reducing ; tending to reduce . 
Inquire into the repentance of thy former life particu- 
larly ; whether it were of a great and perfect grief, and 
productive of fixed resolutions of holy living, and reduc- 
tive of these to act. Jer. Taylor, Holy Dying, iv. 6. 
Reduction reductive. See reduction. Reductive 
conversion, in logic, a conversion of a proposition in 
which there is some modification of the subject or predi- 
cate : as, no man is a mother, therefore no mother is some 
man. See conversion, 2. Reductive principle, a prin- 
ciple by which an indirect syllogism is reduced to a direct 
mood. The reductive principles were said to be conver- 
sion, transposition, and reductio per impossibile. 
II. . That which has the power of reducing. 
So that it should seem there needed no other reductive 
of the numbers of men to an equability than the wars 
that have happened in the world. 
Sir M. Hale, Orig. of Mankind, p. 215. 
reductively (re-duk'tiv-li), adv. By reduction ; 
by consequence. 
Love.and simplicity, and humility,and usefulness: . . . 
I think these do reductively contain all that is excellent 
in the whole conjugation of Christian graces. 
Jer. Taylor, Works (ed. 1835), II. 44. 
reduitt, . See redout 2 . 
redundance (re-dun 'dans), n. [< OF. redon- 
dance, F. rcdondance, rddondancc = Sp. Pg. re- 
dundancia == It. ridondanza, < L. redundantia, 
an overflow, superfluity, excess, < redunda(t-)s, 
redundant: see redundant.] 1. The character 
of being redundant; superfluity; superabun- 
dance. 
He is a poor unwieldy wretch that commits faults out 
of the redundance of his good qualities. 
Steele, Taller, No. 27. 
2. That which is redundant or in excess; any- 
thing superfluous. 
redundancy (re-dun'dan-si), . [As redundance 
(see -cy).] Same as redundance. 
The mere 
Redundancy of youth's contentedness. 
Wordsworth, Prelude, vi. 
= Syn. Verbosity, Tautology, etc. (see pleonasm) ', surplus- 
age. 
redundant (re-dun'daut), a. [<OF. rcdoudant, 
F. redundant, redondant = Sp. Pg. redundante 
= It. ridondante, < L. redundan(t-)s, ppr. of re- 
dinidare, overflow, redound: see redound.] If. 
Rolling or flowing back, as a wave or surge. 
On his rear, 
Circular base of rising folds, that tower'd 
Fold above fold, a surging maze ! his head , . . 
Amidst his circling spires, that on the grass 
Floated redundant. MHlun, P. L., ix. 503. 
