﻿140 The Philippine Journal of Science 1914 



occupy. Way of reading them and writing them. When are they called 

 homogeneous? 



15. Addition, subtraction, multiplication, and division of decimal numbers. 



16. Approximation of the quotient in an inexact division. Reduction of 

 ordinary fractions to decimal and from decimal to ordinary fractions. 



17. Complex and simple numbers. Reduction of a complex number to 

 the simple form. Reduction. Way of making this reduction in the decimal 

 metric system. Reduction from a superior species to another and inter- 

 mediate. 



18. Addition, subtraction, multiplication, and division of complex numbers. 



19. Powers of numbers, roots, exponents. Way of indicating a power. 

 Names that the powers receive and how to form them. 



20. Square root. Cube root. Way of indicating the extraction of roots. 

 Way of finding the square root of an entire number, of a decimal number. 



21. Ratio of numbers, ways of indicating it. Proportion and its funda- 

 mental property. Way of finding one of the means. 



22. Rule of three and its division. Way of solving it. When is it simple 

 and when is it compound? 



23. Partnership. Three cases that may occur and way of solving them. 



24. Rule of alligation. Mode of solving it. When is it direct and when 

 inverse? Interest, how to solve interest when simple and when compound. 



25. Drafts. Different ways of negotiating them. How to find the real 

 value and the nominal value. Discount of a draft and how to find it. 



PRINCIPLES OF GEOGRAPHY AND HISTORY OF SPAIN 



1. Geography: Its divisions. Astronomical geography, heavenly bodies, 

 fixed and errant stars or planets. 



2. Primary planets. What are they? Their double movement. Satel- 

 lites. Comets. Solar system and that of Copernicus. 



3. The sun. Its diameter, volume, and distance from the earth. The 

 moon. Its diameter, volume, and distance from the earth. 



4. The earth, its movements. Meridians, equator, tropics, polar circles, 

 and various zones. Horizon. Cardinal points. 



5. Physical geography. Figure and dimensions of the earth. Continent, 

 island, peninsula, coast, cape, isthmus, mountain, mountain range, desert. 



6. Spring, rivulet, river, torrent, lake, sea, gulf, bay, strait, currents, 

 tides. 



7. Atmosphere and elements that constitute it. Meteors. Winds, clouds, 

 rain, lightning, thunder. 



8. Political geography. Great divisions of the earth. Races of human 

 species. Government and its principal forms. 



9. Europe, its population and location, seas that bound it, its capes, moun- 

 tains, volcanoes, rivers, islands, and principal straits. 



10. Political divisions of Europe. States of the north and their respective 

 capitals. 



11. States in central and southern parts of Europe and their respective 

 capitals. 



12. Spain. Its population, its boundaries, climate, capes, mountain 

 ranges, and main rivers. 



13. Territorial divisions of Spain. Capital of the monarchy. Ultrama- 

 rine possessions and population. 



14. Population, extension, and location of the Philippine Islands. Moun- 



