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So, in the helicopteron, as the helix is at the same time a sustaining plane, it should be likened to a surface moving horizontally, and in which, consequenty, the resistance to motion will be to the lifting power as the sinus is to the cosinus of the angle formed by such plane with the horizon.
1996, Pentti Zetterberg, Matti Eronen, Markus Lindholm, “Construction of a 7500-Year Tree-Ring Record for Scots Pine (Pinus sylvestris, L.) in Northern Fennoscandia and its Application to Growth Variation and Palaeoclimatic Studies”, in Heinrich Spiecker, Kari Mielikäinen, Michael Köhl, Jens Peter Skovsgaard, editors, Growth Trends in European Forests (European Forest Institute Research Report; No. 5), Springer-Verlag Berlin Heidelberg, →ISBN, page 15:
The variations are described in terms of cycles of sinuses and cosinuses.
2007, Vladimir G. Ivancevic, Tijana T. Ivancevic, “Introduction: Human and Computational Mind”, in Computational Mind: A Complex Dynamics Perspective (Studies in Computational Intelligence; 60), Springer-Verlag Berlin Heidelberg, →ISBN, →LCCN, section 1 (Natural Intelligence and Human Mind), pages 60–61:
Basically, the rotation of the matrix of the factor loadings L represents its post-multiplication, i.e. L* = LO by the rotation matrix O, which itself resembles one of the matrices included in the classical rotational Lie groups SO(m) (containing the specific m–fold combination of sinuses and cosinuses.
(anatomy) a pouch or cavity in a bone or other tissue, especially one in the bones of the face or skull connecting with the nasal cavities (the paranasal sinus).
(pathology) an abnormal cavity or passage such as a fistula, leading from a deep-seated infection and discharging pus to the surface.
(trigonometry)sine: in a right triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse.
The mathematical sense ‘chord of an arc, sine’ was introduced in the 12th century by Gherardo of Cremona as a semantic loan from Arabicجَيْب(jayb, “chord, sine”) (ultimately a loan from Sanskritज्या(jyā, “bowstring”)) by confusion with جَيْب(jayb, “bosom, fold in a garment”).
‘‘Come, my companions,’’ she said, ‘‘and with me you all carry back flowers, filling the folds of your garments.’’ (Persephone and her attendants wander away from the protection of her mother Ceres and the other matrons prior to Persephone’s abduction.)
Aeneid (Pūblius Vergilius Marō) lines 1.160–161:
Latin: quibus omnis ab altō // frangitus inque sinūs scindit sēsē͡ unda reductōs.
English: on which all the waves from the deep are broken and it splits itself into receeding ripples.
“sinus”, in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
“sinum”, in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
“sinus”, in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
sinus in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition with additions by D. P. Carpenterius, Adelungius and others, edited by Léopold Favre, 1883–1887)
sinus in Gaffiot, Félix (1934) Dictionnaire illustré latin-français, Hachette.
Carl Meißner, Henry William Auden (1894) Latin Phrase-Book, London: Macmillan and Co.
the heart of the city: sinus urbis (Sall. Cat. 52. 35)
the city is situate on a bay: urbs in sinu sita est
to rejoice in secret: in sinu gaudere (Tusc. 3. 21. 51)
to love and make a bosom friend of a person: aliquem in sinu gestare (aliquis est in sinu alicuius) (Ter. Ad. 4. 5. 75)
(ambiguous) to be driven into the arms of philosophy: in sinum philosophiae compelli
“sinus”, in Harry Thurston Peck, editor (1898), Harper's Dictionary of Classical Antiquities, New York: Harper & Brothers
“sinus”, in William Smith, editor (1854, 1857), A Dictionary of Greek and Roman Geography, volume 1 & 2, London: Walton and Maberly
^ Michiel de Vaan (2008) Etymological Dictionary of Latin and the Other Italic Languages, Leiden: Brill, page 567