Book, Paragraph

 1      I,  7 | genera such as arithmetic and geometry you cannot apply arithmetical
 2      I,  7 |    why it cannot be proved by geometry that opposites fall under
 3      I,  7 |   e.g. as optical theorems to geometry or harmonic theorems to
 4      I,  7 |      theorems to arithmetic). Geometry again cannot prove of lines
 5      I,  10|       in arithmetic units, in geometry points and lines. Both the
 6      I,  10|    and even, square and cube, geometry that of incommensurable,
 7      I,  12|  question will be relevant to geometry, nor to medicine, nor to
 8      I,  12|      proof of the theorems of geometry or of any other science,
 9      I,  12|      the same basic truths as geometry. Of the other sciences the
10      I,  12|     using the basic truths of geometry in conjunction with his
11      I,  12| disputant confines himself to geometry and proves anything from
12      I,  12|  should therefore not discuss geometry among those who are not
13      I,  12|   meaning in the one case not geometry at all, in the other bad
14      I,  12|      at all, in the other bad geometry? It is this error, i.e.
15      I,  13|  problems are subordinated to geometry, mechanical problems to
16      I,  13|       As optics is related to geometry, so another science is related
17      I,  13|     points; e.g. medicine and geometry: it is the physician’s business
18      I,  14| sciences, such as arithmetic, geometry, and optics, and practically
19      I,  27|       exact than and prior to geometry, which requires additional
20      I,  32|     the fundamental truths of geometry, these the fundamentals