(M412) Qu. Why should the magnitude seen at a near distance be deem’d the true one rather than that seen at a farther distance? Why should the sun be thought many 1000 miles rather than one foot in diameter—both being equally apparent diameters? Certainly men judg’d of the sun not in himself, but wth relation to themselves. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M413) 4 Principles whereby to answer objections, viz. 1. Bodies do really exist, tho’ not perceiv’d by us. 2. There is a law or course of nature. 3. Language & knowledge are all about ideas; words stand for nothing else. 4. Nothing can be a proof against one side of a contradiction that bears equally hard upon the other(244). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ What shall I say? Dare I pronounce the admired ἀκρίβεια mathematica, that darling of the age, a trifle? Most certainly no finite extension divisible _ad infinitum_. (M414) Difficulties about concentric circles. (M415) Mem. To examine & accurately discuss the scholium of the 8th definition of Mr. Newton’s(245) Principia. Ridiculous in the mathematicians to despise Sense. Qu. Is it not impossible there should be abstract general ideas? All ideas come from without. They are all particular. The mind, ’tis true, can consider one thing wthout another; but then, considered asunder, they make not 2 ideas. Both together can make but one, as for instance colour & visible extension(246). The end of a mathematical line is nothing. Locke’s argument that the end of his pen is black or white concludes nothing here. Mem. Take care how you pretend to define extension, for fear of the geometers. Qu. Why difficult to imagine a minimum? Ans. Because we are not used to take notice of ’em singly; they not being able singly to pleasure or hurt us, thereby to deserve our regard. Mem. To prove against Keill yt the infinite divisibility of matter makes the half have an equal number of equal parts with the whole. Mem. To examine how far the not comprehending infinites may be admitted as a plea. Qu. Why may not the mathematicians reject all the extensions below the M. as well as the dd, &c., wch are allowed to be something, & consequently may be magnify’d by glasses into inches, feet, &c., as well as the quantities next below the M.? Big, little, and number are the works of the mind. How therefore can ye extension you suppose in Matter be big or little? How can it consist of any number of points? (M416) Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8. Schoolmen compar’d with the mathematicians. Extension is blended wth tangible or visible ideas, & by the mind præscinded therefrom. Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in ye parabola is double the abscisse. Wt need of the utmost accuracy wn the mathematicians own _in rerum natura_ they cannot find anything corresponding wth their nice ideas.