...straight lines AF and BD, and consequently making the angle at G equal to the angle F А С ; and since the three angles of every triangle are equal to two right angles, and since the angles FA С, С AB, BAE, are also equal to two right angles, and since F А С is equal...

...triangles, the four oblique angles of which are equal to the three angles of the triangle, therefore the three angles of every triangle are equal to two right angles. ing the Elements. It proceeds, like that of the French Geometer, by demonstrating, in the first place,...

...not a head for the philosophy of language; and 1 say this with as liltle bad leeling as I say that the three angles of every triangle are equal to two right angles. " That Mr. President Beecher will be immersed in. one of the great American rivers, is now very improbable...

...part of four right angles (Prop. II., Sch. 1), or the third part of two right angles. Also, because the three angles of every triangle are equal to two right angles, the two angles OAB, OBA are together equal to two thirds of two jj^—^C right angles; and since AO is...

...not a head for the philosophy of language : and I say this with as little bad feeling as I say that the three angles of every triangle are equal to two right angles." This is certainly an illustrious specimen of genuine Attic Salt. Dr. Carson, no doubt, has monopolized...

...certainty. In mathematical reasoning, our knowledge is greater than our ignorance. When you have proved that the three angles of every triangle are equal to two right angles, there is an end of doubt; because there are no materials for ignorance to work up into phantoms ; but...

...two angles H i A and '-A HA i ; and because the vertical angles A v H and iv E are equal, and that the three angles of every triangle are equal to two right angles, therefore the two angles VIE and s EH are, together, equal to the two angles AH v and HA i, and therefore...

...If then we can only enunciate, but not conceive, a general proposition, we can never be certain that the three angles of every triangle are equal to two right angles, until it has been demonstrated of triangles of every variety of figure ; and before this can be done,...

...or that the three angles of the triangle before me are together equal to two right angles, because the three angles of every triangle are equal to two right angles. The dictum, then, is obviously one of those selfevident maxims which we have above described, and it may...

...reason of this construction is plain, .. ~~r from Prop. XXXII., Book I., Euclid, which asserts that the three angles of every triangle are equal to two right angles; and from Prop. XIII., Book I., which asserts that the anglet which one straight line mates with anoiJier...