If we next compare one Science with another, the prior and more
accurate of the two is, (1) That which combines at once the [Greek:
o(/ti] and the [Greek: dio/ti]; (2) That which is abstracted from
material conditions, as compared with that which is immersed
therein--for example, arithmetic is more accurate than harmonics;
(3) The more simple as compared with the more complex: thus,
arithmetic is more accurate than geometry, a monad or unit is a
substance without position, whereas a point (more concrete) is a
substance with position.[81] One and the same science is that which
belongs to one and the same generic subject-matter. The premisses of
a demonstration must be included in the same genus with the
conclusion; and where the ultimate premisses are heterogeneous, the
cognition derived from them must be considered as not one but a
compound of several.[82] You may find two or more distinct middle
terms for demonstrating the same conclusion; sometimes out of the
same logical series or table, sometimes out of different tables.[83]
[Footnote 81: Analyt. Post. I. xxvii. p. 87, a. 31-37. Themistius,
Paraphras. p. 60, ed. Speng.: [Greek: kat' a)/llon de\ (tro/pon),
e)a\n ê( me\n peri\ u(pokei/mena/ tina kai\ ai)sthêta\
pragmateu/êtai, ê( de\ peri\ noêta\ kai\ katho/lou.]
Philoponus illustrates this (Schol. p. 235, b. 41, Br.): [Greek:
oi(=on ta\ Theodosi/ou sphairika\ a)kribe/stera/ e)stin e)pistê/mê|
tê=s tô=n Au)tolu/kou peri\ kinoume/nês sphai/ras.] &c.]
[Footnote 82: Analyt. Post. I. xxviii. p. 87, a. 38-b. 5. Themistius,
p. 61: [Greek: dê=lon de\ tou=to gi/netai proi+ou=sin e)pi\ ta\s
a)napodei/ktous a)rcha/s; au(=tai ga\r ei) mêdemi/an e)/choien
sugge/neian, e(/terai ai( e)pistê=mai.]]
[Footnote 83: Analyt. Post. I. xxix. p. 87, b. 5-18. Aristotle gives
an example to illustrate this general doctrine: [Greek: ê(/desthai,
to\ kinei=sthai, to\ ê)remi/zesthai, to\ metaba/llein]. As he
includes these terms und this subject among the topics for
demonstration, it is difficult to see where he would draw a distinct
line between topics for Demonstration and topics for Dialectic.]