De forma et quantitate arcae secundum litteram.
The Shape of the Ark
The author examines the physical shape of Noah's ark, rejecting Origen's tapered design in favor of a structure with four walls and a narrowing roof, and describes the placement of the door and the arrangement of the five levels for animals, food, and dung.
Those who want to examine more closely the truth of what's reported about Noah's ark at the literal level should look into two things in particular: the shape and the size of the ark. Regarding its shape, Origen speaks as follows: "I think, as far as can be gathered from the description, that it rose from the bottom on four corners, and with those same corners gradually drawn inward all the way to the top, it was gathered into the space of one cubit." Several things seem to argue against this opinion: first, that this shape doesn't appear to be well suited for floating. For it's clear that a structure of such great mass, loaded with so many animals and so much provisions, could in no way have floated on the coming waters without being pressed downward by a great part of its own weight; we can still observe the proof of this in ships carrying heavy loads. If then, as is said, it began to contract immediately from the bottom, so that the swelling waves, leaning against the sides from this side and that, would not be repelled but would be received — and the waters would not so much carry the ark as the ark would carry the waters — how could it happen that the whole ark didn't immediately sink to the lowest depths? — and again, when he says: "You will put the opening in the side, downward."✦ The phrase 'downward through the side' seems to signify the side wall, in distinction to the side that was upward in the roof, in which a window was perhaps placed. And again it says: 'Noah, opening the roof of the ark,' reasonably suggests that the ark itself had walls on the lower part, on top of which the roof was placed, and that this roof belonged to the uppermost level, where the person lived, adjoining it. For these reasons, and others of the same kind, it seems to us that within the ark itself, walls were erected in four sections, on top of which the roof was placed, narrowing at its peak to a height of one cubit. How tall the walls themselves were, the text does not say; but so far as we can infer, the height of the walls extended all the way to the base of the fourth level. The teachers affirm that the door of the ark was located between the second and third levels, so that its opening was level with the floor of the third level. Its entrance was cut into the upper side of that same level, so that from the doorway there were two levels below and three above. And they say one level was arranged to receive the animals' dung, and the second for their food. In the third were wild animals; in the fourth, tame animals; in the fifth, which was the highest, were humans and birds. And it's likely that those two lower levels were pressed downward into the waters as the ark floated. But the third story, which held the animals that needed an opening for fresh air, was the first to rise above the waters, so that for anyone climbing up through the water to the ark on the outside, the door would meet them almost at the level of the water's surface. And following this line of reasoning, perhaps the words 'You shall place the door downward' were spoken.✦ Or 'downward' because, no matter which story it was placed in, it was always on the lower side, so that the ark would catch the feet of those entering. But if it's asked whether the height of each individual room was equal or not, we indeed can't prove from authority what ought to be thought about this. In the meantime, we ask only that what isn't contrary to authority be granted to us. We want to distinguish as follows: let's assign to the first room a height of four cubits, to the second five, to the third six, to the fourth seven, to the fifth eight — and so the height of the walls will be fifteen cubits, and the height of the roof fifteen. On the outside walls of this ark, nests or small compartments were built, as if fastened right to the walls themselves, so that their openings could be reached from outside, while the wall remained intact and whole within. And these nests, they say, were made for those animals that can live neither always in water nor always on dry land — like the otter and sea-calves. So much for the shape of the ark.
The Size of the Ark
The literal dimensions of the ark are given as three hundred by fifty by thirty cubits, and the objection that this is too small is resolved by interpreting the cubits as geometric cubits equal to six common cubits, making the ark vast enough to hold the seed-stock of all creatures.
As for its size: the length will be three hundred cubits, the width fifty, and the height thirty. But there are some who say that this size wouldn't have been enough for so many kinds of animals, and for the food they would need to be fed for an entire year. The teachers resolve this question with the following reasoning. They say that Moses — who, as Scripture testifies, had been instructed in all the wisdom of the Egyptians — set down the number of cubits in this passage according to geometry, which the Egyptians especially practice, and by which six cubits are reckoned as one unit.✦ And if this reasoning is applied to the measure of this ark, you'll find such vast spaces of length, width, and height that they could truly have held the seed-stock for restoring the whole world and every living creature — a divine store of seeds. It should also be known that it wasn't necessary to keep in the ark those animals that are not generated by mating but arise from the moisture of the earth or from corpses, or from the decay of any other substance, or those born from the mixing of different species, such as mules and hinnies. From all this it follows that it wouldn't have been impossible for a space of such great capacity to hold the seed-stock for restoring every remaining living creature. But if you'd like to look more carefully into the matters that belong to the geometry of dimensions, a great body of learning shines forth here, and from it we briefly touch on a few points for the sake of keeping things short.
Units of Measurement
The smallest unit of measure is the finger, and from it are derived the palm, the foot, the small cubit, and the great cubit, with the great cubit equaling nine feet, so that the ark's length of three hundred great cubits equals two thousand seven hundred feet.
A finger is the smallest of the country measures that have their own distinct name. Whatever falls short of a finger in terms of these parts, we express as a fraction — one-half, one-third, or one-quarter. This is how we measure by a finger: placing thumb to thumb crosswise, so that the bases of the nails meet along a straight line. By this reckoning four fingers make one palm, and four palms make one foot. A foot and a half make the small cubit; six small cubits make the great cubit; and so the great cubit will have nine feet. The small cubit is one and a half feet. Therefore the length of three hundred great cubits amounts to one thousand eight hundred small cubits. That is two thousand seven hundred feet.
Converting the Ark's Length
The ark's length is converted into palms, digits, paces, stades, and miles, and the method for computing square area and the diagonal of a rectangle is explained.
Ten thousand eight hundred palms, but forty-three thousand two hundred digits. Again, five feet make one pace, one hundred twenty-five paces make one stade, and eight stades make one mile. And from this it's clear that this ark had, in its own length, five hundred forty paces — that is, four stades (half a mile) and forty paces. By a similar method these things can be worked out for the width and the height. And if you'd also like to know how many square units — whether in feet, or in cubits — the area of the ark comes to, multiply the longer side by the shorter, and whatever amount results from that total, that's how many square units the ark is. For example: say fifty times three hundred is fifteen thousand — that's how many square cubits the ark is. And so for other measurements: if you're looking for the diagonal line of this square, here's the rule for you. Multiply each side — that is, the longer one — by itself, then take the sum that results from that, combine it into one side, look for that, and take that as the diagonal.
Diagonal Calculations
Using the dimensions of the ark, the diagonal lines from corner to corner and from the front are computed to be one hundred fifty-two and a half cubits, while the side diagonals are twenty-eight and a half cubits.
For example: Say three hundred times three hundred makes ninety thousand; say fifty times fifty makes two thousand five hundred. The side of this square is three hundred forty-three and one half, that is, not a whole number. If you take half of it, you get one hundred fifty-two and one half minus one. This is the line that stretches from the corner to the middle. If you take this as a base and raise a thirty-cubit beam from the middle of the ark upward, and from that same beam you take fifteen cubits up from the top of the third story, and you treat that as the beam and compare this base to it foot by foot according to the geometrical rule, you'll see, remarkably, all the diagonal corner lines work out to a measure of one hundred fifty-two and a half. In the same way, if you compare the base coming from the front on either side with the beam, you'll also see the diagonals from the front stretching out to one hundred fifty-two and a half. The diagonals that come from the sides, however, will extend to twenty-eight and a half, with bases of twenty-five cubits.
The Hypotemisa and Internal Timbers
The rule for finding the hypotemisa is given, and it is noted that in the ark this corresponds to the oblique timbers stretching from the lowest part to the upper parts.
The rule for finding the hypotemisa is this: multiply the raft-beams by themselves, likewise the base by itself, and combine these sums together, and take the side of that number which results from there as the hypotemisa. In this ark, then, the hypotemisa is represented by timbers stretched out obliquely from the lowest part to the upper parts.
Posts, Bases, and Diagonals
The ratenus is a central post reaching to the top, the base is a line from the corner to the ratenus, and a diagonal runs from corner to corner; some say the ark had only three rooms with a tristega arrangement, and the depicted shape was chosen for ease of showing the wall height.
The ratenus is a post set upright in the middle of the ark, reaching all the way to the top cubit.1 The base is a line lying flat, stretching from the corner of the ark to the ratetum.2 A diagonal line is the name given to the line that stretches from one corner to the corner opposite it. In these triangles and quadrangles you'll find many other things pertaining to geometric subtlety, all of which we're skipping because they'd be tedious. There are others who say there were only three rooms in the ark, and of these, the lowest had one chamber, the middle had two chambers, and the top had three chambers; and they say these distinctions of the rooms are what the Scriptures called "upper rooms," while the three rooms themselves are a tristega.3 And we've depicted this shape rather than the others because we couldn't easily show the height of the walls on a flat surface. For in this shape, the timbers rising from here and there are gradually drawn together until they meet at the peak, at the measure of a single cubit.
Read the original Latin
Qui studiosius indagare cupiunt earum rerum veritatem, quae de arca Noe secundum litteram referuntur, duo praecipue inquirere debent, videlicet formam et quantitatem arcae. Et de forma quidem sic dicit Origenes: « Ego puto quantum ex his quae describuntur apparet, quatuor angulis ex imo consurgentem eisdemque paulatim usque ad summum in augustum attractis in spatium unius cubiti fuisse collectam. » Cui sententiae plura refragari videntur, primum quod haec forma ad natandum non videtur esse idonea. Constat namque tantae molis machinam, tot et tantis onustam animalibus, atque cibariis, nequaquam ita potuisse supernatare venientibus aquis, ut non ex magna parte sui deorsum premeretur; cujus rei experimentum adhuc capere possumus in navibus magna gestantibus onera. Si ergo, ut dicitur, statim ab imo contrahi coepit, ut intumescentes fluctus latera hinc inde inclinantia non repellerent, sed exciperent, et non tam aquae arcam, quam arca aquas portaret? quomodo fieri poterat, ut non tota statim ad ima descenderet; rursum cum dicit. Pones ostium in latere deorsum. Per latus deorsum videtur significare parietem lateralem ad differentiam lateris, quod sursum erat in tecto, in quo fortassis fenestra posita fuit.
Et iterum dicit: Aperiens Noe tectum arcae, satis consequenter innuit ipsam arcam deorsum habuisse parietes, quibus superpositum fuit tectum, quod erat supremae mansioni, in qua homo morabatur, contiguum. Propter has, et alias hujuscemodi causas, videtur nobis quod in ipsa arca parietes in quatuor partibus fuerint erecti quibus tectum superpositum in cacumine suo ad mensuram unius cubiti contraheretur. Cujus autem altitudinis fuerint parietes ipsi, hoc auctoritas non dicit, sed tamen quantum conjicimus altitudo parietum usque ad fundum quartae mansionis extendebatur. Affirmant namque doctores ostium arcae inter secundam et tertiam mansionem locatum, ita ut lumen ejus fundo tertiae mansionis esset contiguum. Introitus autem ejus sursum in latere ejusdem mansionis excisus, ita ut ab ostio duae quidem mansiones deorsum essent, tres vero sursum. Et unam dicunt ad fimum animalium recipiendum ordinatam, secundam ad cibaria eorum. In tertia fuisse indomita animilia, in quarta mitia animalia, in quinta (quae suprema erat) homines et volatilia. Et verisimile est, quod duae illae inferiores mansiones natante arca deorsum inter aquas premerentur.
Tertia vero, in qua animalia erant, quae spiramento aperti aeris eguerunt, prima supra aquas emineret, ita ut foris per aquam ad arcam ascendentibus ostium fere per planum occurreret. Et secundum hunc modum fortassis dictum est: Pones ostium deorsum. Vel deorsum ideo quia in quacunque mansione poneretur, deorsum erat, ut arca intrantium pedes exciperet.
Si vero quaeritur utrum aequalis fuerit altitudo singularum mansionum necne, nos quidem ex auctoritate probare non possumus, quid inde sentiendum sit. Interim tantum, quod auctoritati contrarium non sit, nobis concedi postulamus. Volumus enim sic distinguere, ut primae mansioni demus in altitudine, quatuor cubitos, secundae quinque, tertiae sex, quartae septem, quintae octo, et sic altitudo parietum quindecim habebit cubitos, et quindecim altitudo tecti.
In parietibus hujus arcae foris facti erant nidi sive mansiunculae quasi ad ipsos parietes affixi, ita ut introitus eorum extrinsecus pateret, ipso pariete integro permanente intrinsecus. Et hos nidos dicunt factos esse propter illa animalia, quae nec semper in aqua nec semper in arida degere possunt, sicut est lutra et vituli marini. Haec de forma arcae dicta sunt.
De quantitate dicitur: Trecentorum cubitorum erit longitudo, quinquaginta latitudo, tringinta altitudo. Sed sunt qui dicant, quod haec magnitudo ad tot genera animalium, et ad eorum cibos, quibus per annum integrum vescerentur, capiendos non sufficeret. Quam quaestionem doctores hac ratione solvunt. Aiunt namque quod Moyses, qui ut de eo Scriptura testatur omni sapientia Aegyptiorum fuerat eruditus, secundum autem geometricam, quam praecipue Aegyptii callent, cubitorum numerum in hoc loco posuit, qua in sex cubitis unus deputatur. Quae utique ratio si observetur in hujus arcae mensura, invenientur tanta spatia longitudinis, et latitudinis, et altitudinis, quae vere totius mundi reparanda germina, et universorum animantium capere potuerint re divina seminaria. Sciendum quoque est, quod illa animalia, quae non de coitu generantur, sed de humore terrae vel cadaverum, sive cujuslibet alterius rei corruptione, vel illa, quae ex commistione diversi generis nascuntur, ut muli et burdones, necesse non fuit in arca contineri. Ex quibus colligitur non fuisse impossibile, ut reliquorum omnium animantium seminaria reparanda tantae capacitatis locus contineret. Si autem libet diligentius inquirere ea, quae ad geometricalium dimensionum rationem pertinent, magna hic horum elucet disciplina, ex quibus nos pauca causa brevitatis perstringimus.
Digitus est pars minima agrestium mensurarum propriam appellationem habentium. Quidquid enim digito minus est a partibus respondemus, ut est secunda, tertia vel quarta pars. Per quem videlicet digitum sic mensuramus, ut per transversum pollicem pollici lateraliter conjungentes radices unguium recta linea respondere faciamus. Et haec ratione quatuor digiti faciunt palmum unum, quatuor palmi faciunt pedem unum. Pes et dimidius cubitum parvum, sex parvi cubiti cubitum magnum, et sic magnus cubitus habebit novem pedes. Parvus sesqui pedem. Longitudo ergo trecentorum cubitorum magnorum habebat parvos cubitos mille octingentos. Pedes duo millia, et septingentos.
Palmos autem decem millia et octingentos, digitos vero quadraginta tria [duo] millia ducentos. Rursus quinque pedes faciunt passum unum, centum viginti quinque passus stadium unum, octo stadia milliare unum. Ac per hoc patet, quod haec arca in longitudine sua habuit passus quingentos quadraginta, et stadia quatuor (id est dimidium milliare) et quadraginta passus. Simili ratione possunt ista in latitudine et altitudine reperiri. Quod si etiam scire delectat, quod quadratorum, sive pedum, sive cubitorum fuerit embadion, id est arca, multiplica majus latus per minus, et quot a summa inde excreverit, tot quadratorum erit arca. Verbi gratia: Dic quinquagies trecenti fiunt quindecim millia, tot cubitorum quadratorum est arca. Et sic de aliis: Si hujus tetragoni diagonalem lineam quaeris, haec tibi sit regula. Multiplica utrumque latus, id est majus, unumquodque per se, ac deinde illius summae, quae inde excrescit, in unum coacervatae latus quaere, et hoc prodiagonio habeto.
Verbi gratia. Dic trecenties trecenti fiunt nonaginta millia: Dic quinquagies quinquaginta fiunt duo millia quingenti. Hujus summae latus est trecenti quatuor et semis unum, hoc est non integrum. Si dimidium hujus sumis, habes centum quinquaginta duo et semis uno minus. Haec est, quae extenditur ab angulo usque ad medium. Si hanc habueris pro base, et in medio arcae in altitudinem tringinta cubitorum ratetum erexeris, et de ipso rateto a supremo tertiae mansionis sursum quindecim sumpseris, et hoc pro rateto habueris, eique pedetenus hanc basim secundum geometricalem regulam comparaveris, videbis mirabili ratione omnes angulares hypotemisas in mensuram centum quinquaginta duorum, et semis provenire. Similiter si basim a fronte hinc inde venientem cum rateto contuleris, videbis etiam hypotemisas a frontibus procedentes in centum quinquaginta duo semis porrigi. Quae autem a lateribus veniunt hypotemisae in viginti octo, et semis extendentur habentes bases viginti quinque cubitorum.
Regula inveniendi hypotemisam haec est ut ratetum in se multiplices, similiter basim in se, et has summas simul componas, et illius numeri, qui inde excrescit latus pro hypotemisa habeto. In hac autem arca hypotemisae vicem gerunt tigna oblique ab imo ad superiora porrecta.
Ratenus est stylus in medio arcae erectus usque ad supremum cubitum. Basis est linea jacens ab angulo arcae usque ad ratetum porrecta. Diagonalis linea vocatur, quae protenditur ab angulo in angulum illi oppositum. In trigonis his, et tetragonis multa alia invenies ad subtilitatem geometricae disciplinae pertinentia, quae omnia nos propter fastidium declinamus. Sunt alii, qui dicunt in arca non fuisse nisi tres mansiones, et ex his unam semel cameratam, mediam bicameratam, supremam tricameratam; et aiunt has distinctiones mansionum Scripturarum appellasse caenacula; ipsas autem mansiones tres tristega. Et hanc formam nos idcirco potius quam reliquas depinximus, quia non facile altitudinem parietum in plano demonstrare potuimus. In hac enim forma tigna hinc inde surgentia paulatim contrahuntur donec in cacumine ad unius cubiti mensuram conveniunt.
Scripture echoes
- ↩Gen.6.16 — You shall make a window for the ark, and finish it to a cubit from the top; and the door of the ark you shall set in its side; with lower, second, and third stories you shall make it.
- ↩Gen.6.16 — You shall make a window for the ark, and finish it to a cubit from the top; and the door of the ark you shall set in its side; with lower, second, and third stories you shall make it.
- ↩Acts.7.22 — And Moses was educated in all the wisdom of the Egyptians, and he was mighty in his words and deeds.
Notes
- 1 ↩Ratenus is a rare technical term in this architectural context, likely denoting a central structural post or king-post.
- 2 ↩Ratetum is a rare geometric term, likely referring to the horizontal crossbeam or the baseline of the roof structure.
- 3 ↩Tristega is a rare architectural term for a three-storied structure or a building with three levels.
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