...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 ;...

...any two of its opposite angles shall together be equal to two right angles. Join AC, BD; and because the three angles of every triangle are equal* to two right angles, the three * 32. 1. angles of the triangle CAB, viz. 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. Though this method of treating the subject is strictly demonstrative, yet, as the reasoning in the...

...it is weak. He avows in his severest passages that he has as little angry feeling, as when he says, that " the three angles of every triangle are equal to two right angles ;" but how much more Christian-like may be this cool, apathetic mode of vituperation, the sardonic...

...prospect, before a dark cave, or a dreadful precipice. It is not more evident to the mathematician, that the three angles of every triangle are equal to two right angles, than it is to all mankind, that justice and mercy excel tyranny and oppression. 6. Another desolating...

...proposition, too, would follow the converse of the first one, if ever the sum differed from 180". PROP. III. The three angles of every triangle are equal to' two right angles. B ' Let ABC be any equilateral trlanglfe ; ./\ / \ bisect its angles, which obviously will {[ •£...

...we say it is compelled to affirm, and does affirm this, with the same confidence as the proposition that the three angles of every triangle are equal...not only our highest, but our only idea of truth. Hence, having the idea, or that notion under which it is forced to think of matter, the soul affirms...

...: 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, the three angles of the triangle CAB, viz. the angles CAB, ABC, BCA are equal to two right angles :...

...any two of its opposite angles shall together be equal to two right angles. Join AC, BD. And because the three angles of every triangle are equal to two right angles, (i. 32.) the three angles of the triangle CAB, viz. the angles CAB, ABC, BCA, are equal to two right...

...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...