...right angles;" ire manifestly principles which bear no analogy to such barren <ruunu as these, "Tbiofs that are equal to one and the same thing are equal to one another." " If equals be added to enuals, the wholes are equal." "If equals be taken from equals,...

...moral agents who are susceptible of moral truth ; it comes home to the common sense of all mankind. * " Things that are equal to one and the same thing are equal to each other," — " Two bodies cannot occupy the same space at the same time," are axioms in mathematics...

...right angles ; " are manifestly principles which bear no analogy to such barren truisms as these, " Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals,...

...right angles ; " are manifestly principles which bear no analogy to such barren truisms as these, " Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals,...

...that every magnitude has its half, third, fourth, &c. part. Note. — Though these postulates are act always quoted, the reader will easily perceive where...its part. 3. Every- whole is equal to all its parts taken together. 4. If to equal things equal things be added, the whole will be equal. 5. If from equal...

...angles to others given, be granted as possible : that it is possible for one rightlinetobeperpendicular to another at a given point or distance ; and that...its part. 3. Every whole is equal to all its parts taken together. 4. If to equal things equal things be added, the whole will be equal. . 5. If from...

...two right angles;" are manifestly principles which bear no analogy to such barren truisms as these, "Things that are equal to one and the same thing are equal to one ano" ther." "If equals be added to equals, the whole are equal." "If " equals be taken from equals,...

...third, fourth, A. i . part. - Note. — Though these postulates are not always quoted, the rciuler will easily perceive where and in what sense they...Things that are equal to one and the same thing are t''{lial to each other. 2. Every whole is greater than its part. 3. Every whole is equal to all its...

...right angles ;" are manifestly principles which bear no analogy to such barren trulsmt as these : — " Things that are equal to one and the same thing are equal to one another ;" — " If equals be added to equals, the wholes are equal ;" — " If equals be taken...

...right angles ;" are manifestly principles which bear no analogy to such barren truismo as these : — " Things that are equal to one and the same thing are equal to one another ;" — " If equals be added to equals, the wholes arc equal ;" — " If equals he taken...