# Welsh Journals

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Mathematics* 459 each .of them would be a quarter of it. And so, If you did that 10,000 times with 10,000 other circles, all the right angles would be halves of the very same number, and therefore, all 15 degrees; so, all equal. But I said the answer, H half of 1 go," was true ; so it is clear that our good friend (I mean the Geometer still, not " Long- shanks") did not graduate his circle like a clock, for iso is not the half of 60, but of 360 ; and that makes every right angle 90 degrees (half 180), instead of 15 degrees, (half 30.) As a proof that no particular number must be used, the French have chosen to divide the circle into 400 degrees; a quarter of which being 100, they call their right angles 100—as, of course, they must, when once they have chosen 400 for the whole. So again, our halfoi a right angle must be 45 (half 90), since we have chosen 360; and their half a right angle, must be 50 (half 100), for a similar reason. I have introduced the circle and the axioms here before their time, because they seem quite plain enough for you, but the angles without them are not quite plain enough. We have, as yet, only spoken of the pair of angles being equal. If they are unequal, i.e., if the line, instead of being perpendicular, is what Brother Jona¬ than calls 'J slantendicular," then, clearly, one angle gets more than its share of 900, and the other less; so it would be very wrong to call those " right" angles. It is not fair play then; and they have separate names, as you see in de¬ finition 11 and 12. The "obtuse" or blunt angle has more than 900, and the " acute," or sharp angle, less than 900. Thus, angular space or angular magnitude, is a new sort of quantity, which can be added and subtracted, as well as solids, surfaces, and lines, whereas the poor little point has no magnitude at all, and can only be taken where you find him ; but there is one comfort, that he is always