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  "text": "III. Ossis Bregmatis Giganteæ Magnitudinis Icon; cum Problemate de Gigantis Statura determinanda secundum Regulas Artis Delineatoriae: quae ad Illustre Regalis Societatis Praesidem Dn. Hans Sloane, Bart. transmisit Jac. Theodor. Klein Republ. Gedan. a Secretis & Reg. Soc. Lond. Soc.\n\nEx celebri musco, quod Amstelodami fuit, Wittseniano, os bregmatis giganteum *, cujus altitudo 9 poll. Angl. latitudo 7 (Tab. I.) una cum descriptione & adjuncta figura †, altitudinem capitis a mento ad verticem 20 poll. latitudinem ad tempora 12 poll. (Tab. II.) repraesentante, necnon aliud ejusmodi os, cujus altitudo \\(5 \\frac{6}{8}\\) poll. Angl. latitudo 5 poll. sed sine figura & relatione ad caput anno 1728 nactus, facile invenire potui, assumtis secundum regulas artis delineatoriae octo capitis altitudinibus, staturam gigantis fuisse 13 ped. 4 poll. alterius vero ossis bregmatis, quod insolitum quoque simulabat caput, justam rationem & quidem juxta regulas mathematicas scire cupidus, viro excellentissimo Henrico Kühn, J. U. D. & Athenæi Dantiscani mathef. P. P. meritissimo, sequens proposui Problemata:\n\n* Vid. Catal. Mus. Wittsen. p. 82.\n† A pie defuncto Ruysskio comparatis.\nSi in duobus corporibus humanis diversae statuae fuerit,\n\nIn Priori,\nOssis bregmatis altitudo 9 poll. Angli.\nlatitudo 7.\nIntegri capitis altitudo 20.\nlatitudo 12.\n\nIn Posteriore,\nOssis bregmatis altitudo 5 ½ seu 4 ½ poll. Angl.\nlatitudo 5.\nIntegri capitis altitudo ignota.\nlatitudo ignota.\n\nDeterminare ignotum, & rationem statuae prioris ad posteriorem definire.\n\nCujus Triplex Resolutio, hæc:\n\nSi corpora ista forent similia, res brevissime expediti posset, inferendo; ut in priore corpore, ossis bregmatis altitudo ad integri capitis, vel etiam integri corporis, (tanquam illius octuplam) altitudinem, ita in posteriore corpore, ossis bregmatis altitudo vel latitudo ad integri capitis, vel etiam integri corporis, altitudinem quaestam; quoniam vero 9 ad 7, & 4 ½ ad 5 sunt rationes dissimiles, corpora ista similia non sunt. Quamobrem opus est, ut in calculo & altitudinem & latitudinem ossium bregmatis ratio habeatur; uti ex triplici methodo subjæcta apparebit.\nMethodus Prima.\n\n(Fiat α.) \\(9'' : 20'' = \\frac{46''}{8}\\) : \\(\\left\\{\\begin{array}{l}\n\\text{altitud. capitis quaestam} \\\\\n\\frac{20 \\cdot 46''}{9 \\cdot 8}\n\\end{array}\\right.\\)\n\nerit hujus octuplum \\(= \\frac{8 \\cdot 20 \\cdot 46''}{9 \\cdot 8} = \\frac{20 \\cdot 46''}{9} = \\frac{920''}{9}\\)\n\n\\(= 102 \\frac{2}{9}\\) \\(\\left\\{\\begin{array}{l}\n= 8 \\text{ ped. } 6 \\frac{2}{9} \\text{ poll.} \\\\\n= \\text{staturae corporis secundi.}\n\\end{array}\\right.\\)\n\n(Fiat β.) \\(7'' : 20'' = 5'' : \\frac{100''}{7}\\)\n\nerit hujus octuplum \\(= \\frac{800''}{7} = 114 \\frac{2}{7} = 9 \\text{ ped. } 6 \\frac{2}{7} \\text{ poll.}\\)\n\n\\(= \\text{staturae corporis secundi.}\\)\n\n(Fiat γ.) Staturarum inventarum additio, & summæ bisectio, pro obtinendo medio arithmetico, erit\n\n\\(\\frac{8', 6'' \\frac{2}{9} + 9', 6'' \\frac{2}{7}}{2} = \\frac{17', 12'' \\frac{1}{2}}{2} \\text{ quam prox.}\\)\n\n\\(= \\frac{18' + \\frac{1}{2}''}{2}\\) \\(\\left\\{\\begin{array}{l}\n= 9 \\text{ ped. } \\frac{1}{4} \\text{ poll.} \\\\\n= \\text{structuræ corporis secundi proxime veræ.}\n\\end{array}\\right.\\)\nMethodus Secunda.\n\n(Fiat) \\(9'' - \\frac{1}{7}'' : \\frac{46''}{8} + 5'' = 20''\\) : altitud. capitis posterioris.\n\n\\[\n\\begin{align*}\n\\text{h.e. } & 16 : \\frac{46 + 40}{8} = 20'' : : : : \\\\\n\\end{align*}\n\\]\n\n\\[\n\\begin{align*}\n\\text{h.e. } & 16 : \\frac{86}{8} = 20'' : \\left\\{ \\begin{array}{l}\n\\text{altitud. capitis posterioris} \\\\\n\\frac{20.86''}{16.8} = \\frac{5.86''}{4.8} = \\frac{430''}{32} = \\frac{215''}{16} \\\\\n\\end{array} \\right. \\\\\n\\text{erit hujus octuplum} & = \\frac{8.215''}{16} = \\frac{215''}{2} = 107''\\frac{1}{2} \\\\\n& = 8 \\text{ ped. } 11\\frac{1}{2} \\text{ poll.} \\\\\n& = \\text{staturæ corporis secundi proxime veræ.}\n\\end{align*}\n\\]\n\nId quod cum priori calculo sic satis consentit, cum differentia \\(3\\frac{3}{4}\\) pollicis non excedat.\n\nMethodus Tertia.\n\nQuoniam in diversorum corporum partibus cognominibus (e.g. in duobus ossibus bregmatis) superficies partium sunt inter se, ut quadrata altitudinum corporum integrorum; nec minus superficies istae sint inter se, ut facta ex altitudinibus partium in latitudines: erunt etiam facta ex altitudinibus partium in suas latitudines inter se, ut quadrata altitudinum corporum integrorum. Quare, cum altitudo corporis prioris sit \\(20''\\), adeoque ejus octuplum, seu altitudo in-\nintegri corporis prioris, sit 160'', cujus quadratum est 25600''; fiat\n\n\\[\n\\begin{array}{cccc}\n\\text{altitud. bregmat.} & \\text{prioris.} & \\text{in} & \\text{eius latitud.} \\\\\n9 & 7 & : & \\frac{46}{8} \\\\\n\\end{array}\n\\]\n\n\\[\n\\begin{array}{cccc}\n\\text{altitud. bregm.} & \\text{poter.} & \\text{in} & \\text{eius latitud.} \\\\\n\\end{array}\n\\]\n\n\\[\n\\begin{array}{cccc}\n\\text{quadratum alti-} & \\text{tudinis, prioris} & \\text{corporis integri.} \\\\\n\\end{array}\n\\]\n\n\\[\n\\begin{array}{cccc}\n\\text{quadratum alti-} & \\text{tudinis, poster-} & \\text{rioris corporis} & \\text{integri.} \\\\\n\\end{array}\n\\]\n\n\\[5 = 25600''\\]\n\n\\[\n\\begin{array}{cccc}\n\\text{h.e.} & 63 & : & \\frac{230}{8} = 25600'' : \\frac{230.25600''}{63.8} = \\frac{230.3200''}{63} \\\\\n\\end{array}\n\\]\n\nCum itaque sit \\(\\frac{230.3200''}{63} = \\frac{736000''}{63} = 11682\\frac{1}{2}\\)\n\nquam proxime, = quadrato staturae corporis secundi;\n\nerit (radice quadrata ex 11682 extracta) ipsa corporis secundi statura quam proxime vera = 108 = 9 ped. o poll. Angl. Quae ipsa statura, cum sit inter supra inventas media, pro accuratisima est habenda.\n\nDenique, cum octo capitis altitudines pro statura corporis humani integri satis recte assumere soleamus, & capitis gigantei prioris altitudo sit 20 poll. Angl. erit statura gigantis prioris = 8 . 20'' = 160'' = 13 ped. 4 poll. Angl. Consequentem statura gigantis prioris est ad staturam posterioris, ut 13 pedes, 4 pollices ad 9 pedes in mensura Anglicana, seu ut 160'' ad 180'' seu ut 40 ad 27.\n\nIV. An",
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    "identifier": "jstor-104276",
    "title": "Ossis Bregmatis Giganteae Magnitudinis Icon; cum Problemate de Gigantis Statura Determinanda Secundum Regulas Artis Delineatoriae: Quae ad Illustr. Regalis Societatis Praesidem Dum Hans Sloane, Bart. Transmisit Jac. Theodor. Klein Reipubl. Gedan. a Secretis & Reg. Soc. Lond. Soc.",
    "authors": "Hans Sloane, Jac. Theodor Klein",
    "year": 1739,
    "volume": "41",
    "journal": "Philosophical Transactions (1683-1775)",
    "page_count": 10,
    "jstor_url": "https://www.jstor.org/stable/104276"
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