V: INTRODUCTION TO set up. The PRINCIPIA, above all, glows with the immortality of a transcendant mind. Marble and brass dissolve and pass away ; but the true creations of genius endure, in time and beyond time, forever : high upon the adamant of the indestructible, they send forth afar and near, over the troublous waters of life, a pure, un wavering, quenchless light whereby the myriad myriads of barques, richly laden with reason, intelligence and various faculty, are guided through the night and the storm, by the beetling shore and the hidden rock, the breaker and the shoal, safely into havens calm and secure. To the teacher and the taught, the scholar and the student, the devotee of Science and the worshipper of Truth, the PRINCIPIA must ever continue to be of inestimable value. If to educate means, not so much to store the memory with symbols and facts, as to bring forth the faculties of the soul and develope them to the full by healthy nurture and a hardy discipline, then, what so effec tive to the accomplishment of that end as the study of Geometri cal Synthesis ? The Calculus, in some shape or other, is, indeed, necessary to the successful prosecution of researches in the higher branches of philosophy. But has not the Analytical encroached upon the Synthetical, and Algorithmic Formulae been employed when not requisite, either for the evolution of truth, or even its apter illustration ? To each method belongs, undoubtedly, an appropriate use. Newton, himself the inventor of Fluxions, censured the handling of Geometrical subjects by Algebraical calculations ; and the maturest opinions which he expressed were additionally in favour of the Geometrical Method. His prefer ence, so strongly marked, is not to be reckoned a mere matter oi taste ; and his authority should bear with preponderating weight upon the decision of every instructor in adopting what may be deemed the best plan to insure the completes! mental develop ment. Geometry, the vigorous product of remote time ; blended with the earliest aspirations of Science and the earliest applica tions of Art ; as well in the measures of music as in the move ment of spheres ; as wholly in the structure of the atom as in that of the world; directing MOTION and shaping APPEARANCE; in a wonl, *t the moulding of the created all, is, in comprehensive