...conception of its properties. By attentive consideration we might demonstratively acquire the knowledge, that the sum of its angles is equal to two right angles. Now if another triangle, nearly similar, suppose an isosceles triangle, were presented to us ; if we...

...as soon as he knows what a triangle is, that it has three sides. But he does not know quite so soon that the sum of its angles is equal to two right angles. Hence this proposition becomes to him> at least, synthetic. And yet the equality of its angles, taken...

...given are. 157. ABC is a plano curvilinear triangle formed by arcs of circles which meet in P; shew that the sum of its angles is equal to two right angles. IX. 158. Prove that there may be two, but not more than two, similar triangles in the same segment...

...befall by the eternal decreesof God, and with the same necessity as it follows from the essence of the triangle that the sum of its angles is equal to two right angles. 3rd, Our doctrine furthers and favours the amenities of social life, inasmuch as it teaches us to hate...

...— depend upon our insight into the nature of numbers, form and of figure. We prove, from the nature of a triangle, that the, sum of its angles is equal to two right angles, and from the nature of a circle, that all angles formed in any given arc must be equal and measured...

...follows from God's veracity.* Among things distinctly known Descartes reckons, in the fifth MidiKttton, the facts of extension in space, together with all...inseparable from God's essence, and hence God exists.! In the sixth ileditutimi Descartes concludes from the clear and distinct knowledge which we have of...

...manner, what a triangle or three-sided figure is; yet, all men do not understand the demonstrated truth, that the sum of its angles is equal to two right angles. Evident and certain conclusions, in necessary matter, are seen alike by all person-s that truly know...

...from him, but they follow out of the necessary nature of God, as it follows from the nature of the triangle that the sum of its angles is equal to two right angles (I. prop. 17, sclwl.). They do not come out from him, but remain in him ; just this fact that they...

...or God, as following necessarily out of his nature, or essence. Just as it follows from the nature of a triangle that the sum of its angles is equal to two right angles, so out of the nature of God follow all the modifications of God that we more or less mistakenly look upon...

...conception, say that of a triangle, from the mere conception we can deduce with absolute certainty that the sum of its angles is equal to two right angles. So, too, from the mere idea or con- ' ception of God we can deduce certain properties as necessarily belonging...