octadn.

Brit.

/ˈɒktad/, U.S.

/ˈɑkˌtæd/

Forms: 1800s octade, 1800s– octad.

Origin: A borrowing from Latin. Etymons: Latin octad-, octas.

Etymology: < post-classical Latin octad-, octas the number eight (5th cent.) < ancient Greek ὀκτάδ- , ὀκτάς the number eight, in Hellenistic Greek also a group of eight < ὀκτώ eight (see octo- comb. form) + -άς -ad suffix¹.

1. A group or series of eight things. Originally and chiefly: a set of eight numbers or quantities; spec. (in ancient Greek arithmetical notation) a group of eight characters corresponding to successive powers of ten (analogous to the groups of six figures marking millions, billions, etc., now used); (also) a unit in the Archimedean system of expressing large numbers, representing a power of 10⁸.

ΘΚΠ

the world > relative properties > number > mathematical notation or symbol > [noun] > figure > groupings of figures

bimedial1570

member1608

degree1678

period1678

octad1801

1801 J. Anderson Recreations in Agric. 4 439 If they had adopted the octal; that is, had carried one to the next line at every eight instead of every ten, and had thus counted by octads instead of decads [etc.].

1875 Encycl. Brit. II. 526/2 He [sc. Archimedes] treats of numbers formed by the continued product of that amount [sc. 100,000,000] repeated eight times, extending to sixty-four places in our notation. These he divided into what we should call periods, of eight figures each, to which he gave the name of octades.

1936 Isis 25 23 The older mathematicians ascribed the degree one to the units, the degree two to the tens, and so on. This was already expressed by Archimedes.., who arranged the numbers in octads, respectively in tetrads, in which the units occupied the first rank.

1938 Amer. Jrnl. Bot. 25 283/2 Non-disjunction results in unequal chromosome masses at the poles. Triads, pentads, hexads, and octads..are formed.

1971 M. B. Powell & G. Higman Finite Simple Groups vii. 225 No 5-element set can be contained in two distinct octads, for their symmetric difference would be a -set with at most 6 members.

1995 Brittonia 47 256/1 Three synapomorphies unite the tribe: inflorescence absent.., pedicels ebracteate, and pollen grains shed in octads.

2. Mathematics.

†a. = octave n.² 2d. Obsolete.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > quaternion > system analogous to quaternions

octad1845

1845 J. T. Graves in London, Edinb., & Dublin Philos. Mag. 26 320 As Euler's theorem is connected with Hamilton's quaternions, so my theorem concerning sums of eight squares may be made the basis of a system of octads or sets of eight.

1889 A. Cayley Coll. Math. Papers I. 586 The system of imaginaries..had presented itself to J.T. Graves about Christmas 1843... They are called be him Octads, or Octaves.

b. Geometry. The set of eight points of intersection of three quadric surfaces. rare.

ΘΚΠ

the world > relative properties > number > geometry > surface > [noun] > intersection of > set of eight

octad1870

1870 A. Cayley in Proc. London Math. Soc. 3 20 Suppose that the [quartic] surface has an 8th node:—there are two distinct cases; viz., (1) the 8 nodes are the points of intersection of 3 quadric surfaces, or say they are an octad, and the surface is said to be octadic; [etc.].

1903 Philos. Trans. (Royal Soc.) A. 201 305 It is evident that when two points of an octad coincide, they unite on the Jacobian; and that every point on the Jacobian is the union of a pair of points of an octad.

3. Chemistry. An octavalent element or group. Now rare.

ΘΚΠ

the world > matter > chemistry > valency > [noun] > combining powers of elements > element with the power of eight

octad1868

1868 H. B. Jones & H. Watts Fownes's Man. Elem. Chem. (ed. 10) 470 Manganese..is also said to form a heptachloride, Mn₂Cl₁₄,..according to which it should be regarded as an octad.

1877 H. Watts Fownes's Man. Elem. Chem. (ed. 12) I. 268 Ru[thenium] and Os[mium] form tetroxides (analogous to octochlorides), and may therefore be regarded as octads.

1917 Proc. Royal Soc. 1916–17 A. 93 547 The halogens consequently must act as heptads, sulphur, etc., as octads in the sulphites.., and phosphorus, etc., as nonads in the phosphites.

This entry has been updated (OED Third Edition, March 2004; most recently modified version published online March 2022).

单词	octad
释义	octadn. Brit. /ˈɒktad/, U.S. /ˈɑkˌtæd/ Forms: 1800s octade, 1800s– octad. Origin: A borrowing from Latin. Etymons: Latin octad-, octas. Etymology: < post-classical Latin octad-, octas the number eight (5th cent.) < ancient Greek ὀκτάδ- , ὀκτάς the number eight, in Hellenistic Greek also a group of eight < ὀκτώ eight (see octo- comb. form) + -άς -ad suffix¹. 1. A group or series of eight things. Originally and chiefly: a set of eight numbers or quantities; spec. (in ancient Greek arithmetical notation) a group of eight characters corresponding to successive powers of ten (analogous to the groups of six figures marking millions, billions, etc., now used); (also) a unit in the Archimedean system of expressing large numbers, representing a power of 10⁸. ΘΚΠ the world > relative properties > number > mathematical notation or symbol > [noun] > figure > groupings of figures bimedial1570 member1608 degree1678 period1678 octad1801 1801 J. Anderson Recreations in Agric. 4 439 If they had adopted the octal; that is, had carried one to the next line at every eight instead of every ten, and had thus counted by octads instead of decads [etc.]. 1875 Encycl. Brit. II. 526/2 He [sc. Archimedes] treats of numbers formed by the continued product of that amount [sc. 100,000,000] repeated eight times, extending to sixty-four places in our notation. These he divided into what we should call periods, of eight figures each, to which he gave the name of octades. 1936 Isis 25 23 The older mathematicians ascribed the degree one to the units, the degree two to the tens, and so on. This was already expressed by Archimedes.., who arranged the numbers in octads, respectively in tetrads, in which the units occupied the first rank. 1938 Amer. Jrnl. Bot. 25 283/2 Non-disjunction results in unequal chromosome masses at the poles. Triads, pentads, hexads, and octads..are formed. 1971 M. B. Powell & G. Higman Finite Simple Groups vii. 225 No 5-element set can be contained in two distinct octads, for their symmetric difference would be a -set with at most 6 members. 1995 Brittonia 47 256/1 Three synapomorphies unite the tribe: inflorescence absent.., pedicels ebracteate, and pollen grains shed in octads. 2. Mathematics. †a. = octave n.² 2d. Obsolete. ΘΚΠ the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > quaternion > system analogous to quaternions octad1845 1845 J. T. Graves in London, Edinb., & Dublin Philos. Mag. 26 320 As Euler's theorem is connected with Hamilton's quaternions, so my theorem concerning sums of eight squares may be made the basis of a system of octads or sets of eight. 1889 A. Cayley Coll. Math. Papers I. 586 The system of imaginaries..had presented itself to J.T. Graves about Christmas 1843... They are called be him Octads, or Octaves. b. Geometry. The set of eight points of intersection of three quadric surfaces. rare. ΘΚΠ the world > relative properties > number > geometry > surface > [noun] > intersection of > set of eight octad1870 1870 A. Cayley in Proc. London Math. Soc. 3 20 Suppose that the [quartic] surface has an 8th node:—there are two distinct cases; viz., (1) the 8 nodes are the points of intersection of 3 quadric surfaces, or say they are an octad, and the surface is said to be octadic; [etc.]. 1903 Philos. Trans. (Royal Soc.) A. 201 305 It is evident that when two points of an octad coincide, they unite on the Jacobian; and that every point on the Jacobian is the union of a pair of points of an octad. 3. Chemistry. An octavalent element or group. Now rare. ΘΚΠ the world > matter > chemistry > valency > [noun] > combining powers of elements > element with the power of eight octad1868 1868 H. B. Jones & H. Watts Fownes's Man. Elem. Chem. (ed. 10) 470 Manganese..is also said to form a heptachloride, Mn₂Cl₁₄,..according to which it should be regarded as an octad. 1877 H. Watts Fownes's Man. Elem. Chem. (ed. 12) I. 268 Ru[thenium] and Os[mium] form tetroxides (analogous to octochlorides), and may therefore be regarded as octads. 1917 Proc. Royal Soc. 1916–17 A. 93 547 The halogens consequently must act as heptads, sulphur, etc., as octads in the sulphites.., and phosphorus, etc., as nonads in the phosphites. This entry has been updated (OED Third Edition, March 2004; most recently modified version published online March 2022). < n.1801
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