544 THE POPULAR SCIENCE MONTHLY. 



book : JEst multitudo ex unitatihus composita (is multitude composed 

 of units). And, again, in the third part of his first book he says : 

 Seriem numero et in infinitum posse procedere lit quocuinque oiu- 

 mero dato dari potest major unitatem addendo. (A series in number 

 may go on to infinity, so that any given number may be made larger 

 by adding unity.) And in this way number is an aggregation or col- 

 lection of one or many units. And to proceed in infinitum by the ad- 

 dition of one. From which it appears that unity is not number ; but, 

 on the contrary, is the root and foundation of numbers. Even as 

 Boethius says in his arithmetic. Nevertheless, one is higher and more 

 perfect than all the numbers that are. For in it are united potentially 

 the property and perfection of all numbers. And without it nothing 

 can have being. And Euclid, at the beginning of the seventh book, 

 says : TJnitas est qua una quacumque res una dicitur (Unity is that 

 by which any one thing is called one). And the logicians say that one 

 is one of the six transcendent principles. For it comprehends all things 

 that have being. Then, again, it has all the property of number. For 

 it is perfect, like six, it is lineal, square, cube, solid,, square root, cube 

 root, root of root. And because it is of so great dignity and excel- 

 lence, the Creator has chosen it for his essence ; for he is one only 

 God, creator of all the world. A good law, to wit : the Christian law, 

 divided into ten commandments. And a good faith : to wit, the Catho- 

 lic faith, divided into twelve articles. And so many other dignities 

 and perfections. 



" Two is a number of so great pre-eminence and utility that God 

 has kept it in mind in many of his works. For first, he created light 

 and darkness. Then he created two great lights, to wit, the sun and 

 the moon. The sun, to light the day; and the moon, to light the night. 

 Then he created all beasts in two sexes, to wit, masculine and femi- 

 nine ; and made for them several double members, to wit, two eyes, 

 two ears, two nostrils, two arms, two hands, two legs, two feet and 

 many others of utility to the human body. And then, as many pas- 

 sions as the human body suffers, such as joy and sadness, hope and 

 fear, hunger and thirst, heat and cold, drinking and eating, sleeping 

 and waking, health and sickness, living and dying, and all relative 

 qualities are also constituted in duplicity, as creator and creature, 

 parent and son, creating and created, producing and produced, ab- 

 stract and concrete, etc. And also all opposites, as kindness and mal- 

 ice, virtue and vice, knowledge and ignorance, wisdom and foolishness, 

 truth and falsehood, etc. And we think that after unity more things 

 are found constituted by two than by any superior number. 



"Three is the most worthy and most perfect, after one, that is 

 among the numbers. Thus, as says almost every one's maxim, Om7ie 

 trinum perfectum (Every trine is perfect). And the perfection does 

 not proceed by the composition of it, as it does of six. But by the 

 great and high mysteries that are found in this number. And first, it 



