Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/288

 which depart from two points marked upon another right line, are then wider above than below, when the angles included between them upon that right line are greater than two right angles; and if these angles should be equal to two right angles, the lines would be parallels; but if they were less than two right angles, the lines would be concurrent, and being continued out would undoubtedly intersect the triangle.

Without taking it upon trust from you, I know the same; and am not so very naked of Geometry, as not to know a Proposition, which I have had occasion of reading very often in Aristotle, that is, that the three angles of all triangles are equall to two right angles: so that if I take in my Figure the triangle ABE, it being supposed that the line EA is right; I very well conceive, that its three angles A, E, B, are equal to two right angles; and that consequently the two angles E and A are lesse than two right angles, so much as is the angle B. Whereupon widening the lines AB and EB (still keeping them from moving out of the points A and E) untill that the angle conteined by them towards the parts B, disappear, the two angles beneath shall be equal to two right angles, and those lines shall be reduced to parallels: and if one should proceed to enlarge them yet more, the angles at the points E and A would become greater than two right angles.

You are an Archimedes, and have freed me from the expence of more words in declaring to you, that whensoever the calculations make the two angles A and E to be greater than two right angles, the observations without more adoe will prove erroneous. This is that which I had a desire that you should perfectly understand, and which I doubted that I was not able so to make out, as that a meer Peripatetick Philosopher might attain to the certain knowledg thereof. Now let us go on to what remains. And re-assuming that which even now you granted me, namely, that the new star could not possibly be in many places, but in one alone, when ever the supputations made upon the observations of these Astronomers do not assign it the same place, its necessary that it be an errour in the observations, that is, either in taking the altitudes of the pole, or in taking the elevations of the star, or in the one or other working. Now for that in the many workings made with the combinations two by two, there are very few of the observations that do agree to place the star in the same situation; therefore these few onely may happily be the non-erroneous, but the others are all absolutely false.

It will be necessary then to give more credit to these few alone, than to all the rest together, and because you say, that these which accord are very few, and I amongst these 12, do find two that so accord, which both make the distance of the