problem 
3f. In English universities, a public disputation. 
- Absolute problem, see atortute. Alhazen's prob- 
lem, the problem from two given points in the plane of a 
given circle to draw linea intersecting on the circumfer- 
ence and making equal angles with the tangent at the 
point of intersection. ApolloniUB's problem, the prob- 
li'in to draw a circle tangent to three given circlet in a 
plane. This celebrated problem was proposed, accord- 
ing to I'appus, by Apollonius in his work on contacts. 
Busschop's problems, the following problems : (1) to 
cut a square into eight pieces which will fit together to 
make two squares, one twice as large as the other ; (2) to 
cut a regular hexagon into five parts which will make a 
square ; (3) to cut a regular pentagon into seven parts 
which will make a square. Characteristic problem. 
See characteristic. Chess problem, a given position of 
chess pieces in which it is required that one side mate 
the other (or sometimes compel the other to give mate) in 
a stipulated number of moves. Comparative prob- 
lem, a question In regard to the degree of any quali- 
ty possessed by any subject. Crown, Delian, deter- 
minate problem. See the qualifying words. For- 
mat's problem, given two media separated by a plane 
and the velocities of light in Hum, to Hint the path of 
quickest transmission between two given points. Flor- 
entine, goniometrtcal, imperial, indeterminate, in- 
verse problem. See the adjectives. Gergonne's prob- 
lem, the problem to cut a cube so that the section shall 
enter at a diagonal of one face and emerge at the non- 
parallel diagonal of the opposite face, making the surface 
of section the smallest possible. Huy gens's problem, a 
problem proposed by Christian Huygens In }in>, to this 
effect : a given number of perfectly elastic spheres lie in 
one straight line; the masses of the first and last are 
known ; the flrst strikes the second with a given velocity : 
what must the masses of the Intermediate ones l>e to make 
the velocity imparted to the last a maximum? This was 
solved by Huygens for three bodies, by Lagrange in 1750 
for li v r, and by Picart in 1874 completely. Isoperimet- 
rlcal problem, a problem relating to a maximum or 
minimum condition to be fulfilled by the form of a func- 
tion : so called because the earliest problems of this kind 
were of isoperimetry in the narrower sense. Kepler's 
problem, the problem from a given point on the diam- 
eter of a semicircle to draw a line dividing the area in a 
given proportion ; to solve the equation a = x - 6 sin x ; 
to find the position of a planet at a given time from it - 
elements. This problem, of capital importance, was pro. 
posed by Kepler in 1801). L'Hulliers problems, the 
following problems : (1) to cut a given triangular prism 
so that the plane section shall be equal to a given triangle ; 
(2) on a given triangle as base to erect an oblique prism 
so that the perpendicular section shall be similar to a 
given triangle. Limited problem, in math., a problem 
that has but one solution, or some determinate number 
of solutions. Linear, local, notional problem. See 
the adjectives. Malfatti's problem, a problem of cle 
mentary geometry, mentioned by 1'appiis about 300, but 
first solved by Oianfrancesco Malfatti (1731-1807) in 1788: 
namely, to inscribe In a given triangle three circles, each 
touching two sides of the triangle, and all tangent to one 
another. The best construction was given by Stelner in 
1826. Mechanical solution of a problem. See me- 
chanical. Nonius's problem, the problem to find the 
day of shortest twilight for a given latitude. Pap- 
pus's problem, in a given circle to inscribe a triangle 
whose sides produced shall contain three given points. 
Pell's problem, tin' problem to solve the equation 
xz - Ay = B. Petersburg problem, a celebrated 
problem in probabilities, to determine how much ought 
to be paid for the assurance of being paid >"', where m is 
tin 1 number of times that a coin will be tossed up without 
coming up head: so called because mentioned by Daniel 
Bernoulli in the Memoirs of the St. Petersburg Academy, 
but already treated by Nicolas Bernoulli the first in 1713. 
Pfaff's problem, the problem to transform an expres- 
sion X i ax\ + .\-_. dr.,. . . . into another of similar 
form with a given number of terms, and to determine the 
smallest possible number of terms. Pothenot's prob- 
lem, to find a point from which two given segments are 
Been under given angles. Problem of duration of 
play, to find the probability that one player will ruin 
another within a given number of bets, and the probable 
number of bets before he is ruined. Problem of 
squaring the circle. See umiarinsr. Problem of the 
couriers, see courier. Problem of the duplication. 
See dupticatutii. Problem of the inscription of the 
heptagon, the impossible problem to inscribe a regu- 
lar heptagon in a circle with a rule and compass. 
Problem of the school-girls, the problem to show 
how fifteen school-girls might walk out in ranks of three 
every day for a week, without any one walking a second 
time in the same rank with any other. Problem of three 
bodies, the problem to determine the motions of three 
mutually gravitating particles Sursolld problem, in 
mat ft., a problem which cannot be resolved but by curves 
of a higher kind than the conic sections. Vlvlanl's 
problem, to pierce a hemispherical dome with four equal 
windows so that the rest of the surface shall be quad- 
rable. 
problematic (prob-le-mat'ik), a. [= F. pro- 
bttmatique = Sp. problemdtico = Pg. It. proble- 
matico, < L. problematictis, < Or. irpo/jfa/fiaTiKof, 
pertaining to a problem, < irp6(ftri[ia(r-), a prob- 
lem: see problem.'] 1 . Of the nature of a prob- 
lem; questionable; uncertain; unsettled; dis- 
putable; doubtful. 
The probability of foreign rivalry was not believed in, or 
was treated as at least distant and problematic. 
W. R. Grey, Misc. Essays, 1st ser., p. 3. 
2. Iii totjif, of the nature of a question, pos- 
sible or doubtful. 
1 call a concept problematic if It is not self-contradic- 
tory, and if, as limiting other concepts, it is connected with 
other kinds of knowledge, while its objective reality can- 
not be known in any way. . . . The concept of a noume- 
non is problematical that is. the representation of a thing 
of which we can neither say that it Is possible nor that it 
is impossible, because we have no conception of any kind 
4743 
of Intuition but that of our senses, or of any kind of con- 
cepts but of our categories, neither of them being appli 
came to any extrasensuous object. 
Kant, Critique of Pure Reason (tr. by Miiller), ill. 
Problematic proposition. See proporitian. 
problematical iprob-le-mat'i-kal), a. [< prob- 
lematic + -al.] Same ttsprobteiiialic. 
Wagers are laid In the city about our success, which Is 
yet, as the French call It, problematical. 
Johnion, to Mrs. Thrale, NOT. 1, 1777. 
problematically (prob-le-mat'i-kal-i), adv. [< 
problematical + Wy 2 .] In a problematic man- 
ner; doubtfully; dubiously; uncertainly. 
problematist (prob'lem-a-tiat), n. [< Gr. vpo- 
,tf.^a(r-), a problem, 4- -w<.] One who pro- 
poses problems. [Rare.] 
This learned problematist. 
Evelyn, To Dr. fieale, Aug. 27, 1668. 
problematize (prob'lem-a-tiz), v. i.; pret. and 
pp. problematized, ppr. problematizing. [< Gr. 
jrpo / 3>.tf/j(r-), a problem, 4- -i?e.] To propose 
problems. 
Tip. Hear him problcmatwe. 
Pru. Bless us, what's that? 
Tiii. Or syllogize, elenchlie. B. J onion. New Inn, II. 2. 
pro bono publico (pro bo'no pub'li-ko). [L. : 
pro, for; 00/10, abl. of bonum, good; publico, 
abl. of publicus, public : see pro, boua, public.] 
For the public good. 
Proboscidse (pro-bos'i-de), . pi. [NL., for 
'I'roboscid idse,<. Gr. irpofioanii; (-KIO-), proboscis, 
4- -id.] The family of the elephants: now 
called Klephantidif. 
proboscidal (pro-bos'i-dal), a. [< L. proboscis 
(-cid-), < Gr. rrpo.ioaKtf (-*5-), proboscis, + -al.] 
Same as proboscidiform. 
A proboKvtal prolongation of the oral organs. Shtideard. 
proboscidate (pro-bos'i-dat), a. [< L. proboscis 
(-cid-),(. Gr. Trpn/loaulf (-KIO-), proboscis, + -ate 1 .] 
Having a proboscis; proboscidean Probosci- 
date insect, an Insect having a prol>osc!dat mouth. 
Proboscidate mouth, in tntow.. a hanstellate mouth ; a 
mouth In which the organs are modified to form a probos- 
cis, as In most flies. See cut under hmuc-fty. 
proboscide (pro-bos'id), . [< F. proboscide, 
< L. proboscis, proboscis : see proboscis.] In 
her., the trunk of an elephant used as a bear- 
ing or part of a bearing. 
Proboscidea (pro-bo-sid'e-S), i. pi. [NL. (Illi- 
ger, 1811), < L. proboscis (-cid-), < Gr. rrpOjlooKif 
(-wd-), proboscis: see proboscis."] 1. An order 
of Mammalia having a long flexible proboscis 
or trunk. It now contains only the elephants and 
their allies, as the mammoths and mastodons. The legs 
are mostly exserted beyond the common integument of 
the trunk, and all their joints are extensible in a right 
line. The teeth are enameled; the incisors are In the 
living elephants two above and none below, In some ex- 
tinct Probntcidfa none above and two below, or two 
above and below, any of which may be developed Into 
long tusks curving out of the mouth. The feet are all 
five-toed, so far as is known, incased in broad shallow 
hoofs, one to each digit, and the palmar and plantar 
surfaces are padded. The carpal nones are broad and 
short, in two separate, not interlocking, rows ; the scaphoid 
and lunar are separate from each other ; the cuneiform is 
broad, extended Inward, and attached to the ulna ; the 
unciform is directly in front of the cuneiform, and the 
magnum In front of the lunar; in the hind foot the as- 
tragalus articulates In front only with the navlcular. I lie 
placenta is deciduate, eonary. The Proboncidca belong to 
the higher or edncablllan series of placenta! mammals. 
Their nearest living relatives are the Hyracmdea. There 
arc 2 families Elepkantidie, containing the elephants, 
mammoths, and mastodons, and Ltiiwtheriidte, the dino- 
there*, the latter all extinct, the former now represented 
by only 2 living species. See cuts under Vinathrrium, 
elephant, Klrphantintr, and MastodontintF. 
2. A class of corticate protozoans, also called 
Rhynchoflagellata, represented by the noctilu- 
caiis. E. R. Lankester. 
proboscidean (pro-bo-sid'e-an), a. and n. [< 
L. proboscis (-cid-). < Gr. irpo/ioanif (-<5-), pro- 
boscis, 4- --an.] I. a. 1. Having a proboscis 
or trunk; proboscidate or proboscidif erous ; 
belonging to the mammalian order Probo- 
scidea. 2. Of or pertaining to a proboscis: as, 
'the proboscidean sheath of the Nemertines," 
Encuc. Brit., XXIV. 184. 
Also proboscidial, proboscoid. 
Proboscidean flukes, the trematoids of the family TV- 
trarhynchiiijf. 
II. n. A mammal of the order Proboscidea ; 
an elephantid or dinotheriid. 
Also proboscidian. 
proboscideous (pro-bo-sid'e-ns), a. [< L. pro- 
hnxi'i.1 (-cid-), < Gr. irpofiooiat (-KIO-), proboscis. 
-I- -eoux.] In bot., having a hard terminal 
horn, as the fruit of ifartynia. Treasury of 
Botany. 
proboscides, ". Latin plural of proboscis. 
proboscidial (prd-bo-sid'i-al), a. [< L. probos- 
cis (-cid-), < Gr. xpoliooKie, (-ud-), proboscis, + 
-/'.] Same as proboscidean. 
probouleutic 
proboscidian (pro-bo-sid'i-an), a. and w. [< 
L. proboscis (-rid-), < Gr. npo/ioonif (-<)-), pro- 
boscis, + -tan.] Same as proboscidean. 
Proboscidif era ( pro-bos-i-dif ' e-rii),fi.j>f. [NL., 
neut. pi. of proboscidif er : see proboscidiferovs.] 
A division of pectinibranchiate gastropods with 
a small head, a proboscis retractile under the 
base of the tentacles, and variable teeth on a 
long cartilaginous lingual ribbon, it includes a 
large number of carnivorous gastropods, among the best- 
known of which are the Muriciilir and the llvccinitltr, 
Contrasted with Kottr\fera. 
proboscidiferous (pro-bos-i-dif'e-rus), a. [< 
NL. proboscidif er, < L. proboscis (-cid-), probos- 
cis, + ferre = E. bear 1 .] 1. Having a probos- 
cis. 2. In couch., pertaining to the Probosci- 
difera. 
prbboscidiform (pro-bos'i-di-fomi), a. [< L. 
proboscis (-cid-), proboscis, 4- forma, form.] 
Proboscis-like. Also probopcidal. /irobosciform, 
probosciformed. 
probosciform (pro-bos'i-form). a. [< L. pro- 
boscis, proboscis, + forma, form . ] Same as pro- 
boscidiform. Kncyc. Diet. 
probosciformed (pro-bos'i-fdrmd), a. [< pro- 
bosciform + -ed"*.] Same as proboscidij 'arm. 
The surface of ihepnbotcif armed month, facing the flrst 
pair of cirri, has a deep central longitudinal fold. 
Darn-in, CirrlpedU, p. 176. 
Probosciger (pro-bos'i-jer), w. [NL. (Kuhl, 
1820), < L. proboscis, proboscis, + gerere, carry.] 
A genus of black cockatoos: synonymous with 
Microglnxsa. 
proboscigerous ( pro-bo-si j'e-rus), a. [< L. pro- 
boscis, proboscis, + gerere, carry.] Having a 
proboscis ; proboscidiferous. 
proboscis (pro-bos'is), .; pi. proboscides (-i- 
dez). [== F. 'proboscide = Sp. proMncide = Pg. 
proboscis = It. proboscide, proboscis, < L. pro- 
boscis, < Gr. ;rpo,j<x7k/'f (-<5-), the trunk or pro- 
boscis of an elephant, the proboscis of a fly, 
an arm of a cuttlefish, < rrpo, before, + ftoaxetv, 
feed, graze.] 1. An elephant's trunk; hence, 
a long flexible snout, as the tapir's, or the 
nose of the proboscis-monkey. See cut under 
Xasalis. 
The unwieldy elephant, 
To make them mirth, used all his might, and wreathed 
His lithe probotcu. Milton, P. I.., iv. 347. 
2. Any proboscidiform part or organ; anything 
that sticks out in front of an animal like an ele- 
phant's trunk. See cut under CjfttopkorilUB. (a) 
The human nose, especially when very large. [ Humorous. | 
(6) In enlom. : (1) The rostrum or beak of a rhynchoph- 
orous beetle, or snout-beetle. (2) The long coiled haus- 
tellate organ of leptdopterous Insects ; an antlia. See cut 
under hautteUum. (3) The sucking-mouth of a fly, a cylin- 
drical membranous or fleshy organ terminating in a dilated 
portion which is applied to the substance to l>e sucked up. 
(See prnunari*, and cut under houtt-fly.) (4) The extensi- 
ble mouth-organs of a bee, consisting of the labium and 
lingua with their various divisions, and the maxillie, united 
at their bases with the labium. (r) In Vennes, a divers!' 
form buccal, oral, or pharyngeal organ of many worms, 
as errant annelids, gephyreans, turnellarians, and nemer- 
teans. In the last the proboscis is a tubular invaginated 
everslble organ opening in the anterior part of the body 
above the mouth, formed by a differentiation of the In- 
tegument : it is variable In details of structure : it may 
be divided, coiled, glandulous, and furnished with stylets, 
a retractor muscle, etc. (For various proboscides of this 
kind, see cuts under Acanthocephala, Balantigloitfiwt, Cet- 
toidet, Kereif, Proctucha, Jihabaocaela, and Khynchoeceia.) 
(d) In conch., the tongue of certain gastropods, such as 
shell-snails, when it is so long as to be capable of being 
protruded for some distance from the mouth, in which 
case It is used for boring the shells of other testaceans, 
and for destroying by suction the soft parts of the in- 
habitant: distinguished from roxfruin. () In polyps, the 
central polyplte of a mednsan. (/) In gregarines, the 
epimerite. 
proboscis-monkey (pro-bos'is-mung'ki), n. A 
semnopithecine ape, A'asalis larratus; a ka- 
liaii : so called from the elongated and flexible 
snout- which resembles the human nose in size 
and shape. See cut under Xasalis. 
proboscis-rat (pro-bos'is-rat), n. Same as tie- 
pliant-shrew. 
proboscoid (prp-bos'koid), a. [< Gr. vpoOoanif, 
proboscis, 4- rMor, form.] Same as proboscid- 
ean. 
probouleutic (pro-b^-ln'tik), a. [< Gr. vpo3oi- 
(-fcvr-), previous deliberation (cf. MGr. 
mfr, one who deliberates before), < 
irpoBavMietv, contrive before, < irpo, before, 4- 
[iavMfaiv, take counsel, deliberate: see boul< 2 .] 
Concerned with the preparation of measures 
for action: noting specifically the Senate, or 
Council of Five Hundred, in the ancient Athe- 
nian constitution. 
A misapprehension as to the powers of the Roman Senate, 
which is represented as being a protmtlrutic body, like 
that of Athens, whieh prepared business for the Assembly. 
IT. F. Allen, Penn. Monthly, Feb., 1879, p. 124. 
