...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 phantasms; but...

...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 phantasms ;...

...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 ;...

...grounds. There are some, of which we can say that we know them ; others, that we believe them. We know that the three angles of every triangle are equal to two right angles. We do not doubt that there is such a country as England, and that such a king as Henry VIII. formerly...

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

...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 phantasms; but...

...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...

...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...

...; any two of its opposite angles are together equal to two right angles. Join AC, BD ; and because the three angles of every triangle are equal to two right angles (1. 32), the three angles of the triangle CAB, namely, the angles CAB, ABC, BCA, are equal to two right...

...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,...