projectiveadj.n.
/prəˈdʒɛktɪv/, U.S. /prəˈdʒɛktɪv/, /proʊˈdʒɛktɪv/ A. adj.† 1. Scheming, inventive. Obsolete.† 4. Jutting or sticking out; projecting. Obsolete.
ΘΚΠ
the mind > will > intention > planning > [adjective]
imaginativec1405
compassingc1440
contrivinga1616
projective1640
designing1656
scheming1838
planful1862
organizatory1917
1640 R. Brome Sparagus Garden i. iii. sig. B4v You have a wit sir Hugh, and a projective one; what, have you some new project a foot now?
a1652 R. Brome Court Begger ii. i. sig. P3v, in Five New Playes (1653) They have all projective braines I tell you. Men. Pray of what nature are your Projects Gentlemen?
1729 J. Mitchell Poems Several Occasions I. 253 The humbled Nation, now, too late, In dire Effects its Folly finds; We mourn the Mis'ry of our State, And curse the rash, projective, Minds.
2. Mathematics.† c. Of a geometrical figure: capable of being obtained from another by projection. Obsolete. rare.
a. Of, relating to, or produced by the projection of lines or figures on a surface. Now rare.
ΘΚΠ
the world > relative properties > number > geometry > [adjective] > of geometrical relation
reciprocal1570
regular1570
projectivea1652
semi-conjugate axis1743
homographic1859
symmetric1860
confocal1867
correlative1881
involutorial1885
conjugate1902
antisymmetrical1913
homoeomorphic1918
homotopic1918
isometric1952
a1652 S. Foster Elliptical Horologiography (1654) 171 How upon any plain to draw an Ellipticall Diall, to an Index set any way, by Sphericall (and not Projective) work.
1710 J. Harris Lexicon Technicum II Projective Dialling, is the way of Drawing, by a method of Projection, the true Hour-lines, Furniture of Dials, &c. on any kind of Surface whatsoever.
?1785 Artist's Assistant in Study Mech. Sci. (new ed.) 39 Perspective is..employed in representing the ichnographies, and ground-plots of objects as projective planes.
1894 Westm. Gaz. 14 June 7/1 A lady exhibitor demonstrating an ingenious projective goniometer. By means of this instrument..the projection of a crystal on a sphere is accomplished.
1986 Leonardo 19 61/1 Conventional projective drawings..proved inadequate because I could not, using them, produce a drawing that would allow me to ‘see’ simultaneously all sides of the atrium.
b. Relating to or involving an algebraic operation analogous to geometrical projection, esp. one in which objects (such as vectors) are determined only up to a scale factor; of or relating to a projective space or projective geometry.
ΚΠ
1854 Philos. Trans. (Royal Soc.) 144 61 Nearly all of the projective properties of right lines and conic sections on a plane may be transformed into analogous properties of great circles and spherical conic sections on the surface of a sphere.
1888 Amer. Jrnl. Math. 10 302 To find the linear homogeneous Gr in R4, we must write the projective groups in R3 homogeneous and linear in x1....x4.
1918 O. Veblen & J. W. Young Projective Geom. II. iii. 72 Any projective collineation transforming a Euclidean plane into itself is said to be affine.
1965 J. J. Rotman Theory of Groups viii. 161 The projective unimodular group PSL (m, k) is the group SL(m, k)/Z0.
1972 M. Kline Math. Thought xxxviii. 907 Seeking to show that metrical notions can be formulated in projective terms he [sc. Cayley] concentrated on the relation of Euclidean to projective geometry.
1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xxiv. 537 To Chasles was due the emphasis in projective geometry on the six cross ratios..of four collinear points or four concurrent lines, and the invariance of these under projective transformations.
ΘΚΠ
the world > relative properties > number > geometry > [adjective] > of geometrical relation > from which others derive
primitive1728
fundamental1832
projective1885
1885 C. Leudesdorf tr. L. Cremona Elements Projective Geom. 107 If P is the point of intersection of QS and RT, then ATPR is a projection of ACA′B′ from Q as centre, and ATPR is also a projection of ABA′C′ from S as centre; therefore the group ACA′B′ is projective with ABA′C′, and therefore..with A′C′AB.
3. † b. Having the power of projecting or throwing itself forward with energy. Obsolete. rare.
a. Of or relating to projection or casting forth; that throws forwards or onwards; projecting, propelling. Now rare.
ΘΚΠ
the world > movement > impelling or driving > [adjective] > propulsive
remigial1592
propellant1644
propulsive1648
propulsory1656
protrusive1676
projectile1696
projective1697
propelling1710
elastic1712
propulsatory1826
1697 W. Molyneux Let. 20 July in J. Locke Corr. (1981) VI. 165 I doubt not but Sir R. Blacmore..had a regard to the proportionment of the Projective Motion to the Vis Centripeta.
1705 C. Purshall Ess. Mechanism Macrocosm xxii. 166 The Attractive Power of the Sun at A, is turn'd towards r: but there the Projective Force being too strong for the Attractive Power, it breaks out.
1718 E. Strother Criticon Febrium (ed. 2) Introd. 18 An equal Projective Force will push an equal Body obliquely upward with less Resistance and more Celerity, than if it were mov'd upward in a Perpendicular.
1781 C. Lofft Eudosia 141 The Comets know their period, still not all Perhaps revolve; some the projective force Through countless worlds, and systems without end, May hurry.
1844 Proc. Amer. Philos. Soc. 1841–3 2 205 If it be further assumed, that the projective force is not only dependent on the pressure at the time of the explosion, but also on the specific gravity of the gases.
1848 P. J. Bailey Festus (ed. 3) 217 From the projective moment of all light The moon was in the sun, and in the sun The form of earth was.
1953 S. F. Mason Main Currents Sci. Thought iii. xiv. 117 The Aristotelians of the middle ages were of the view that a projectile moved at first upwards along an inclined straight line until the projective force was exhausted, and then it fell vertically downwards.
1990 Technol. & Culture 31 404 It was well understood that the projective force of gunpowder was due to the sudden release of a large quantity of elastic fluid.
ΚΠ
1861 J. Brown Horæ Subsecivæ 2nd Ser. II. 101 His fiery, projective, subtle spirit, could not linger in the outer fields of mere observation.
ΘΚΠ
the world > space > shape > unevenness > projection or prominence > [adjective]
steepc1000
tooting?c1225
strutting1387
prominent?1440
extant1540
eminent?1541
pouting1563
poking1566
out1576
egregious1578
promontory1579
out-pointed1585
buttinga1593
outjetting1598
perking1598
jettying1609
juttying1609
out-jutting1611
outstanding1611
upsticking1611
out-shooting1622
jutting1624
outgrowing1625
rank1625
toting1645
projectinga1652
porrected1653
protruded1654
protruding1654
upcast1658
protending1659
jettinga1661
raised1663
starting1680
emersed1686
exerted1697
projective1703
jet-out1709
exorbitant1715
sticking1715
foreright1736
poky1754
perked-up1779
salient1789
prouda1800
overdriven1812
extrusive1816
stand-up1818
shouldering1824
jutty1827
outflung1830
sticky-out1839
sticking-up1852
outreaching1853
protrusive1858
out-thrusting1869
stickout1884
protrudent1891
1703 R. Neve City & Countrey Purchaser 20 This Jutty, or projective Building.
1756 tr. M.-A. Laugier Ess. Archit. i. 34 These inequalities in an entablature continued, are not excusable, but when by the meeting of a projective or unequal front it is prudent to have an interruption there.
1798 G. L. Leclerc Nat. Hist. IV. 222 The crangon, or shrimp, with long slender feelers, and between them two projective laminae.
1844 E. B. Barrett Lett. R. H. Horne (1877) II. lxi. 167 Thin colourless lips, fit for incisive meanings—a nose and chin projective without breadth.
5. Of or relating to mental projection.
a. Having the quality of being projected by the mind, or the power of so projecting.
ΘΚΠ
the mind > mental capacity > perception or cognition > faculty of imagination > [adjective] > conveying to the mind
representativea1475
projectivea1839
visual1868
a1839 S. T. Coleridge & J. Gillman Hints towards Theory of Life (1848) 80 There is an equal intensity both of the immanent and the projective reproduction.
1908 Edinb. Rev. Jan. 200 Kingsley's practical qualities (including a quite genuine projective imagination) were out of all proportion to the reflective.
1949 C. E. M. Joad Shaw viii. 232 St. Catherine, God, the Virgin..are merely creatures of our incorrigibly dramatic imagination which..projects them on to the canvas of an empty universe and then proceeds to hail..the creations of its own projective faculty.
2000 Amer. Jrnl. Psychol. 113 463 Much of his biology was more a projective statement about his own beliefs than an objective account of the brain.
b. Psychology. Of or relating to the projection of unconscious feelings, fears, fantasies or desires; esp. designating a test designed to reveal unconscious elements of personality by responses to words or images.
ΘΚΠ
the mind > mental capacity > psychology > psychology of personality > testing of personality > [adjective]
projective1895
psychodiagnostic1909
the mind > mental capacity > psychology > study of emotions > [adjective] > projecting unconscious feelings
projective1895
1895 J. M. Baldwin Mental Devel. vi. 120 All of them [sc. stages of attitude] belong in the ‘projective’ stage of the child's sense of self, i.e., they all go to furnish data which he afterwards appropriates to himself as ‘subject’.
1956 A. I. Hallowell in B. Klopfer et al. Devel. Rorschach Technique II. xiv. 476 Rorschach theory, as well as that underlying other projective tests, has been based on the general assumption..that ‘every subject's responses..are determined by psychological attributes of that subject’.
1971 Jrnl. Gen. Psychol. 84 321 The clinician using the auditory method is now able to consider stimulus properties when evaluating projective material.
1999 M. L. Silverstein Self-Psychol. & Diagnostic Assessm. ii. iv. 82 The process of listening to projective test responses requires examiners to keep the range of clinical inferences broad rather than narrow.
6. Of poetry or poets: characterized by or using ‘open’ or ‘natural’ forms as a means of reflecting aspects of the spontaneous process of composition (such as the poet breathing), in contrast to the formal ‘closed’ structures of traditional poetry. Frequently in projective verse.
ΘΚΠ
society > leisure > the arts > literature > poetry > poem or piece of poetry > types of poem according to form > [noun] > verse designed to show inherent energy
projective verse1950
1950 C. Olson in Poetry N.Y. iii. 15 Projective verse teaches, is, this lesson, that that verse will only do in which a poet manages to register both the acquisitions of his ear and the pressures of his breath.
1950 C. Olson in Poetry N.Y. iii. 22 Eliot..has only gone from his fine ear outward rather than, as I say a projective poet will, down through the workings of his own throat to that place where breath comes from, where breath has its beginnings, where drama has to come from, where, the coincidence is, all art springs.
1963 Listener 7 Mar. 435/3 A poet I liked very much is Robert Bly. In versification he is not ‘projective’, but in tone and attitude he is.
1967 Book Week (Washington Post) 19 Mar. 6/1 Here what he [sc. Olson] calls the Projective Open or Field verse (as opposed to the systematic Closed Forms of the past) is put to work, using line, syllable, breath, as principles he has preached. His one theme is energy—how a man's energy is expended in history and in space.
1985 20th Cent. Lit. 31 326 Long before..the prophets of projective verse attempted to formulate a poetics of breath, E. M. Forster was advocating a humanism with a voice audible to all who listened.
1992 N.Y. Rev. Bks. 24 Sept. 66/4 No doubt Helgerson could explain that Projective Verse was an attempt to take over the American Constitution.
B. n.
Psychology. A projective test (see A. 5b).
ΘΚΠ
the mind > mental capacity > psychology > psychology of personality > testing of personality > [noun] > projective test
Thematic Apperception Test1935
projection test1946
TAT1946
projective1950
1950 Amer. Sociol. Rev. 15 593/1 The claim that projectives and other tests may be used to validate analyses made by other ethnological methods must be qualified.
1976 L. R. Aiken Psychol. Testing & Assessm. (rev. ed.) viii. 223 Questionnaires and projectives are useful, but the most popular psychometric device for determining attitudes is an attitude scale.
2004 J. W. Pettit in M. Hersen & J. C. Thomas Psychopathology in Workplace iv. 53 Projectives provide a means of avoiding the denial bias yet are plagued by poor psychometric properties.
Compounds
projective geometry n. the branch of geometry concerned with projective properties; the geometry of projective spaces.
ΘΚΠ
the world > relative properties > number > geometry > [noun] > branches of
planimetrya1393
conic?a1560
helicosophy1570
stereometry1570
spheric1660
planometry1669
mensuration1704
polygonometry1791
analytical geometry1802
isoperimetry1811
analytic geometry1817
algebraic geometry1821
coordinate geometry1837
non-Euclidean geometry1872
differential geometry1877
pangeometry1878
projective geometry1878
metageometry1890
Riemann geometry1895
variable geometry1957
1878 Amer. Jrnl. Math. 1 272 The projective geometry is proved to be independent of the theorem of parallels.
1911 J. W. Young Lect. Fund. Concepts Algebra & Geom. xiii. 135 It [sc. the term ‘metric geometry’] serves to distinguish this geometry from the so-called projective geometry or the geometry of position, as it is sometimes called, which is entirely independent of the notion of measurement, and involves only the various intersectional properties of points, lines, planes, etc.
2004 N.Y. Times (National ed.) 26 Aug. b1/3 Mr. Stork and Mr. Criminisi applied projective geometry to one of the arms of the Arnolfini chandelier to see what the others should look like given the various angles that the painter would have seen them from.
projective identification n. Psychoanalysis the process by which (usually negative) aspects of a person's personality are projected on to and identified with another person, sometimes resulting in interactions through which the recipient actually feels or acts on the projected trait or emotion.
ΚΠ
1949 A. Koestler Insight & Outlook vi. 81 Between the two extremes of projective identification and aggressive derogation stretches a continuous spectrum of the emotive effects of representative art.
1952 M. Klein in J. Riviere Devel. in Psycho-anal. ix. 300 Much of the hatred against parts of the self is now directed towards the mother. This leads to a particular form of identification which establishes the prototype of an aggressive object-relation. I suggest for these processes the term ‘projective identification’.
1999 A. M. Pines Falling in Love x. 170 A man who learned to deny his dependence and need for intimacy projects them onto his wife who then seems even more needy and dependent than she really is. Projective identification makes both of them identify with the respective projections.
projective plane n. Mathematics a two-dimensional manifold which may be regarded as the space of straight lines through the origin of three-dimensional space, or as a spherical shell with all pairs of antipodal points identified (each straight line through the sphere's centre projecting two antipodal points at which it intersects the spherical shell on to a single point of the plane).
ΘΚΠ
the world > space > [noun] > projective space > projective plane
projective plane1899
1899 Science 3 Nov. 654/2 Lines and envelopes of straight lines on a projective plane.
1962 B. H. Arnold Intuitive Concepts Elem. Topol. iii. 71 A projective plane can be considered as a disk and a Möbius strip whose edges are joined.
1975 I. Stewart Concepts Mod. Math. xiii. 199 This is exactly what is happening in the projective plane: going round once things get twisted; going round twice brings them back to normal.
projective property n. Mathematics a property (of a figure) which remains unchanged after projection.
ΚΠ
1854 Philos. Trans. (Royal Soc.) 144 61 Nearly all of the projective properties of right lines and conic sections on a plane may be transformed into analogous properties of great circles and spherical conic sections on the surface of a sphere.
1931 V. F. Lensen Nature of Physical Theory 53 The concept of projective properties presupposes that of the straight line, but not of length. The projective properties are unchanged by a projective transformation.
1997 J. V. Field Invention of Infinity vii. 202 Perspective is not being seen as a procedure that ‘degrades’ but merely as one that transforms, leaving certain relationships the same. The relations that are left the same are what we now call ‘projective properties’ of the figure concerned.
projective space n. Mathematics a space which may be regarded as obtained by taking a vector space of the next higher dimension, identifying all vectors which are multiples of one another, and omitting the origin.
ΘΚΠ
the world > space > [noun] > projective space
projective space1900
1900 Amer. Jrnl. Math. 22 336 The bilateral projective space is the ordinary projective space, while the unilateral projective space Rn is in effect the space of rays diverging from a point in metric space Rn+1.
1960 P. J. Hilton & S. Wylie Homology Theory iii. 133 The real projective space Pn may be defined as the image of the n-sphere Sn under identification of all pairs of antipodal points.
1992 J. G. Oxley Matroid Theory vi. 165 Every finite projective space can be regarded as a matroid.
Derivatives
proˈjectively adv.
ΘΚΠ
the world > movement > impelling or driving > [adverb] > so as to propel
projectively1703
the world > relative properties > number > geometry > [adverb] > in specific way
incongruously1656
projectively1703
unicursally1892
the mind > mental capacity > perception or cognition > faculty of imagination > [adverb] > by projection
projectively1703
1703 W. Freke Lingua Tersancta v. 45 With Fear when not follow'd, projectively avoid things in vain.
1856 Proc. Royal Soc. 8 107 The two images coalesce..; as soon as they coincide, the lateral curvature of the vertical lines ceases, and they are bent projectively from back to front.
1871 T. L. Cuyler Heart-Life 39 He follows Jesus so heartily, so projectively, that he carries others along with him by his sheer momentum.
1957 N. Frye Sound & Poetry 96 To say that it is a structure of sound which ‘has a meaning’ is harmless enough, but it is speaking, as the psychologists now say, ‘projectively’.
1997 Australian (Nexis) 18 Apr. (Features section) 12 Jade projectively imagines what Tracy's last sight and understanding of the world must have been as she was packraped and bashed to death.
This entry has been updated (OED Third Edition, June 2007; most recently modified version published online March 2022).
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adj.n.1640