Philosophical poems by Henry More ...

Cant. 2.

STANZ. 5. Or like a Lamp, &c,

See Plotin. 'Ennead. 4. lib. 1. cap. 8. & 12.

STANZ. 24. Withouten body having energie.

'Tis the opinion of Plotinus. 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉.

Ennead. 4. lib. 1.

STANZ. 57. But if't consist of points then a Sca∣lene I'll prove all one with an I∣sosceles, &c.

If quantity consists of Indivisibles or Atoms, it will follow that a Scalenum is all one with an Isosceles, &c.

Before I prove this and the following conclusions, it will be necessary to set down some few Axioms and De∣finitions:

Axioms.

1.That a Line hath but two ends.

2.That Lines that consist of an equall number of A∣toms, are equall.

3.That it is indifferent where we pitch upon the first Line in a superficies, so that we fill the whole Area, with Lines parallell to what first we choose.

4.That no Motion goeth on lesse, then an Atom at a time, or the breadth of a Mathematicall Line.

Definitions.

1.An Isosceles, is a Triangle having two equall sides.

2.A Scalenum, is a Triangle having all sides unequall.

Theorem. 1.

That a Scalenum, and an Isosceles, be all one.

[illustration] diagram

Let ABC be a Scalenum; The same ABC is also an Isosceles. For fill the whole Area ABC with Lines par∣rallell to AC by the 3. Axiom. There is then as many points in BA as in BC by the 1. Axiom; and therefore by the second, BA is equall to BC. and consequently by the 1. Definition. ABC is an Isosceles.

Appendices.

The same reason will prove. 1. That every Triangle is an Isopleuron or equilaterall Trirngle. 2. That the Diametre of a Quadrangle is equall to any of its sides. 3. That the Chord of a segment of a Circle, is equall to the Ark, &c.

Vers. 4. That the crosse Lines of a Rhomboids, That from their meeting to all corners presse, be of one length.

Theorem. 2.

That the diagoniall Lines of a Rhombeids be equall.

[illustration] diagram

Let ACBD be a Rhomboides, and AB stretch'd out in infinitum, after the infinite productions of CB and AD. I say, that DC will be equall to AB. For EC is equall to EA, and ED to EB, by the precedent Theorem. Wherefore DC and AB are equall.

The same is also as briefly prov'd by the first or second Appendix of the precedent Theorem.

STANZ. 58. And with her grasping rayes, &c.

Theorem. 3.

That the Moon sometimes enlightens the whole Earth, and the Sunne sometimes enlightens not the Earth at all.

To prove this, I must set down some received Pro∣positions in Opticks and Astronomie.

Propositions Opticall.

1.SPhaeriodes luminosum minus si propinquius est opaco, minorem portionem illustrat quam si remotius existat.

2.Sphaeroides luminosum majus ê propinquo ampliorem partem opaci irradiat quam ê remoto. Aguilon. lib. 5.

Propositions Astronom.

1.THe greatest distance of the Full or New Moon, from the Centre of the Earth, is 64. semi∣diameters of the Earth.

2.The least distance of the Moon New or Full, from the Centre of the Earth, is 54. semidiame∣ters of the Earth: so that there is five Diameters difference.

3.The Sun in his Apo∣gee, is distant from the Centre of the Earth 1550 semidiameters of the Earth, but in his Perigee 1446. So there is 52. Diameters difference.

Now let B be the Moons Perigee, A her Apogee, CEGD, the Earth enlightned so farre as DE, by the Moon at B. Let the Moon be now removed from B into A. By this removall into A, the Earth CEGD will be more enlightned

[illustration] lunar diagram

by the first propositions Opticall. But I say CEGD is enlightend all over by the Moon in A, for the di∣stance AB is five times bigger then the Diameter CG from the Consect. of the first and second propositions Astronomicall. But HG is but part of CG, so that AB will be above five times bigger then GH, to which also EG is but equall by the first and second Axiom, or the third appendix of the first Theorem. Wherefore there is above five times as ma∣ny Atoms in AB as in EG. But in every Atom re∣move from B toward A, the light, has gaind an Atom in EG by the fourth Axiom. Therefore the Moon at B has enlightned the Earth CDGD even unto the utmost point G, long before it be removed to A: so that CDGD when the Moon has got to A will be swallowed over and over again into the Moons rayes.

But now for the second part of the Theorem. That the Sunne sometimes enlightens not the earth at all.

Let the Sunne be in his Perigee A, enlightening the Earth CEHD so farre as FG. Remove him from A to his Apogee B. In his recession to B the Earth CEHD is lesse and lesse enlightned by the second Opticall Proposition, I say, it is not en∣lightned at all.

For suppose he had gone back but the length of IC, then had FCG been devoyd of light, be∣cause that CG hath no more points in it then IC hath, by the first and second Axiom. or third Appendix of the first Theorem. And the light cannot go off lesse then an Atom a time by the fourth Axiom. Much more destitute therefore is the Earth CHED of light, the Sunne being in B, when as the distance

AB will measure above fif∣ty times CH (which yet is bigger then IC) by the Consect. of the third propo∣sition Astrnomicall, so that day will hang in the sky many thousand miles off from us, fastigiated into one conicall point, and we be∣come utterly destitute of light.

[illustration] solar diagram

A man might as well with placing the Sunne in B first prove him to enlighten all the Earth at once, and make perfect day.

As also the Moon if you place her in her Apogee first, that she enlightens not the least particle of the Earth though in her full.

Lastly, if you place them in K you might prove they do enlighten every part and never a part of the Earth at once, so that a perfect Uni∣versall darknesse and light would possesse the World at the same time, which is little better then a pure con∣tradiction. Thematter is ve∣ry plain at the first sight.

STANZ. 28. In every place, &c.

〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. Ennead 2. lib. 9. cap. 7.