NIC. You ſay truth.

RIC. I have another queſtion to aske you, which is this, Why the Author

uſeth the word Liquid, or Humid, inſtead of Water.

uſeth the word Liquid, or Humid, inſtead of Water.

NIC. It may be for two of theſe two Cauſes; the one is, that Water being the

principal of all Liquids, therefore ſaying Humidum he is to be underſtood to mean

the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of

this Book of his, do not only hold true in Water, but alſo in every other Liquid,

as in Wine, Oyl, and the like: and therefore the Author might have uſed the word

Humidum, as being a word more general than Aqua.

principal of all Liquids, therefore ſaying Humidum he is to be underſtood to mean

the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of

this Book of his, do not only hold true in Water, but alſo in every other Liquid,

as in Wine, Oyl, and the like: and therefore the Author might have uſed the word

Humidum, as being a word more general than Aqua.

RIC. This I underſtand, therefore let us come to the firſt Propoſition, which, as

you know, in the Original ſpeaks in this manner.

you know, in the Original ſpeaks in this manner.

PROP. I. THEOR. I.

If any Superficies ſhall be cut by a Plane thorough any

Point, and the Section be alwaies the Circumference

of a Circle, whoſe Center is the ſaid Point: that Su

perficies ſhall be Spherical.

Point, and the Section be alwaies the Circumference

of a Circle, whoſe Center is the ſaid Point: that Su

perficies ſhall be Spherical.

Let any Superficies be cut at pleaſure by a Plane thorow the

Point K; and let the Section alwaies deſcribe the Circumfe

rence of a Circle that hath for its Center the Point K: I ſay,

that that ſame Superficies is Sphærical. For were it poſſible that the

ſaid Superficies were not Sphærical, then all the Lines drawn

through the ſaid Point K unto that Superficies would not be equal,

Let therefore A and B be two

Points in the ſaid Superficies, ſo that

228[Figure 228]

drawing the two Lines K A and

K B, let them, if poſſible, be une

qual: Then by theſe two Lines let

a Plane be drawn cutting the ſaid

Superficies, and let the Section in

the Superficies make the Line

D A B G: Now this Line D A B G

is, by our pre-ſuppoſal, a Circle, and

the Center thereof is the Point K, for ſuch the ſaid Superficies was

ſuppoſed to be. Therefore the two Lines K A and K B are equal:

But they were alſo ſuppoſed to be unequal; which is impoſſible:

It followeth therefore, of neceſſity, that the ſaid Superficies be

Sphærical, that is, the Superficies of a Sphære.

Point K; and let the Section alwaies deſcribe the Circumfe

rence of a Circle that hath for its Center the Point K: I ſay,

that that ſame Superficies is Sphærical. For were it poſſible that the

ſaid Superficies were not Sphærical, then all the Lines drawn

through the ſaid Point K unto that Superficies would not be equal,

Let therefore A and B be two

Points in the ſaid Superficies, ſo that

228[Figure 228]

drawing the two Lines K A and

K B, let them, if poſſible, be une

qual: Then by theſe two Lines let

a Plane be drawn cutting the ſaid

Superficies, and let the Section in

the Superficies make the Line

D A B G: Now this Line D A B G

is, by our pre-ſuppoſal, a Circle, and

the Center thereof is the Point K, for ſuch the ſaid Superficies was

ſuppoſed to be. Therefore the two Lines K A and K B are equal:

But they were alſo ſuppoſed to be unequal; which is impoſſible:

It followeth therefore, of neceſſity, that the ſaid Superficies be

Sphærical, that is, the Superficies of a Sphære.

RIC. I underſtand you very well; now let us proceed to the ſecond Propoſition,

which, you know, runs thus.

which, you know, runs thus.