Today | News | Books | Recipes Adventure | Science Fiction | Ghost stories | Poetry | Children | History Bookof years (such as 20, 40, or 60 years at once) is allowed for, such years are called _anni collecti_. For example, a period of 27 years includes 20 years _taken together_, and 7 separate or _expanse_ years. The mean motion during smaller periods of time, such as months, days, and hours, is added in afterwards. 45. Here the author enters a little more into particulars. If the mean motion be required for the year 1400, 3 years later than the starting-point, look for 3 in the table of expanse years, and add the result to the number already corresponding to the 'root,' which is calculated for the last day of December, 1397. Allow for months and days afterwards. For a date earlier than 1397 the process is just reversed, involving subtraction instead of addition. 46. This article is probably not Chaucer's. It is found in MS. Bodley 619, and in MS. Addit. 29250. The text is from the former of these, collated with the latter. What it asserts comes to this. Suppose it be noted, that at a given place, there is a full flood when the moon is in a certain quarter; say, e.g. when the moon is due east. And suppose that, at the time of observation, the moon's actual longitude is such that it is in the first point of Cancer. Make the label point due east; then bring the first point of Cancer to the east by turning the _Rete_ a quarter of the way round. Let the sun at the time be in the first point of Leo, and bring the label over this point by the motion of the label only, keeping the _Rete_ fixed. The label then points nearly to the 32nd degree near the letter Q, or about S.E. by E.; shewing that the sun is S.E. by E. (and the moon consequently due E.) at about 4 A.M. In fact, the article merely asserts that the moon's place in the sky is known from the sun's place, if the difference of their longitudes be known. At the time of conjunction, the moon and sun are together, and the difference of their longitudes is zero, which much simplifies the problem. If there is a flood tide when the moon is in the E., there is another when it comes to the W., so that there is high water _twice_ a day. It may be doubted whether this proposition is of much practical utility. 41_a_: This comes to precisely the same as Art. 41, but is expressed with a slight difference. See fig. 16, where, if _bc_ = 8, then BC = 12/8 EB. 41_b_: Merely another repetition of Art. 41. It is hard to see why it should be thus repeated in almost the same words. If _bc_ = 8 in fig. 16, then EB = 8/12 BC = 2/3 BC. The only difference is that it inverts the equation in the last article.] 42_a_ This is only a particular case of Art. 42. If we can get _bc_ = 3, and _b'c'_ = 4, the equations become EB = 4BC, E'B = 3BC; whence EE' = BC, a very convenient result. See fig. 17.] 43_a_: The reading _versam_ (as in the MS.) is absurd. We must also read '_nat_ come,' as, if the base were approachable, no such trouble need be taken; see Art. 41. In fact, the present article is a mere repetition of Art. 43, with different numbers, and with a slight difference in the method of expressing the result. In fig. 18, if _b'c'_ = 3, _bc_ = 4, we have E'B = 3/12 BC, EB = 4/12 BC; or, subtracting, EE' = (4-3)/12 BC; or BC = 12 EE'. Then add the height of E, viz. E_a_, which = AB. 42_b._: Here, 'by the craft of _Umbra Recta_' signifies, by a method similar to that in the last article, for which purpose the numbers must be adapted for computation by the _umbra recta_. Moreover, it is clear, from fig. 17, that the numbers 4 and 3 (in lines 2 and 4) must be transposed. If the side parallel to _b_E be called _nm_, and _mn_, E_c_ be produced to meet in _o_, then _mo_ : _m_E :: _b_E : _bc_; or _mo_ : 12 :: 12 : _bc_; or _mo_ = 144, divided by _bc_ (= 3) = 48. Similarly, _m'o'_ = 144, divided by _b'c'_ (= 4) = 36. And, as in the last article, the difference of these is to 12, as the space EE' is to the altitude. This is nothing but Art. 42 in a rather clumsier shape. Hence it appears that there are here but 3 independent propositions, viz. those in articles 41, 42, and 43, corresponding to figs. 16, 17, and 18 respectively. Arts. 41_a_ and 41_b_ are mere repetitions of 41; 42_a_ and 42_b_, of 42; and 43_a_, of 43. CRITICAL NOTES. As, in the preceding pages which contain the text, the lower portion of each page is occupied with a running commentary, such Critical Notes upon the text as seem to be most necessary are here subjoined. TITLE. Tractatus, &c.; adopted from the colophon. MS. F has 'tractatus astrolabii.' A second title, 'Bred and mylk for childeren,' is in MSS. B. and E. [The MSS. are as follows:--A. Cambridge Univ. Lib. Dd. 3. 53.--B. Bodley, E Museo 54.--C. Rawlinson 1370.--D. Ashmole 391.--E. Bodley 619.--F. Corpus 424.--G. Trin. Coll. Cam. R. 15. 18.--H. Sloane 314.--I. Sloane 261.--K. Rawlinson Misc. 3.--L. Addit. 23002. (B. M.)--M. St. John's Coll. Cam.--N. Digby 72.--O. Ashmole 360.--P. Camb. Univ. Lib. Dd. 12. 51.--Q. Ashmole 393.--R. Egerton 2622 (B. M.).--S. Addit. 29250 (B. M.) See the descriptions of them in the Introduction.] PROLOGUE. l. 26. thise B; þese C; _miswritten_ this A; see above, ll. 21, 22. 32. curious BC; _miswritten_ curios A. Many similar very slight alterations of spelling have been silently made in the text, and are not worth specifying here. A complete list of them is given in my edition of this treatise for the Early English Text Society. I give, however, the real variations of reading. Thus, in l. 58, A. has _som_ for _sonne_; and in l. 64 omits the second _the_. PART I. § 1, l. 3. wol B; wolde AC. § 2, l. 2. _Rowm_ is here an adjective, meaning _large_, _ample_. It is the right reading; we find Rowm AB rowme C; rvm M. § 3, l. 1. AB _omit_ the. § 9, l. 3. nombre AB; nou_m_bre C; _but_ nombres _in old editions_. § 12, l. 5. The MSS. all[60] read--'_vmbra recta_ or elles _vmbra extensa_, & the nether partie is cleped the _vmbra versa_.' This is certainly wrong. § 13, l. 2. a certein] _so in_ AB; CM _omit_ a. But Chaucer certainly uses the phrase 'a certain'; cf. 'of unces a certain,' C. T., G 776; and see G 1024. § 14, ll. 2, 5. The word _halt_ for _holdeth_, and the expression _to-hepe_, together, both occur in Troil. iii. 1764:-- 'And lost were al, that Love _halt_ now _to-hepe_.' § 17, l. 1. principal C; tropikal AB; M _om._ The reading _tropikal_ is absurd, because there are but _two_ such; besides which, see l. 34 below. 17. the nyht (_over an erasure_) B; thee nyht (_over an erasure_) A; þe ni[gh]tes C; þe ny[gh]tes M. § 20, l. 4. figure; _here (and sometimes elsewhere) miswritten_ vig_ur_ A. Throughout the whole treatise, the scribe has commonly written 'vig_ur_'; in many places, it has been corrected to 'fig_ur_e.' § 21, l. 15. the (_before_ sterres) _supplied from_ BC. 27. where as C; wher AB. 56. ou_er_keruyd A; ou_er_kerued B; ou_er_kerueth (_the latter part of the word over an erasure_) C; _first time only_. PART II. § 2, l. 8. eu_er_ M; euere C; eu_er_y (_wrong |