Analyses of Boohs. 67 



principles of hydrostatics. *' A merchant ship is generally designed 

 to carry a great quantity of weight in proportion to its length and 

 breadth, that is, to its general buoyance, and this great weight is 

 stowed nearly throughout the length instead of being contracted in 

 the middle of the vessel, where its effects to cause pitching and 

 scending would be much less. Therefore, the double disadvantage 

 of great weight, and that weight being stowed in the extremities, 

 which are subject to be very unequally supported in a head sea, 

 requires that the bows of many merchant ships should have nearly 

 as much area as can be given to prevent them, when loaded, from 

 pitching deeply and dangerously in a head sea, and if the breadth of 

 the stern and fulness of the quarter be in proportion to the area of 

 the bow, motion of scending or plunging the stern into the water 

 will be also avoided." 



In a country like ours, where prosperity and navigation are so in- 

 timately allied, every hint from practical men, in reference to the 

 construction of ships, should be carefully treasured up. 



IV. — On the Theory of Ratio and Proportion, as treated by 

 Euclid, including an inquiry into the nature of quantity. 

 By the Rev. Baden Powell, M.A., F.R.S., &c. 



This forms a communication, by the author (one of the most active 

 and promising members of the University of Oxford) 'to the Ash- 

 molean Society. The author's object in this tract is to defend 

 Euclid from the charges of inconsistency which have been brought 

 against him by Sir John Leslie and others, in consequence of the 

 introduction of the doctrine of ratio and proportion as part of his 

 system of geometry. Most of the best writers of geometry (as Le- 

 gendre) omit this part in their elementary systems, and most teachers 

 in this country pass over the 5th book, and adopting the doctrine of 

 proportionals from algebra, proceed to apply it to the theorems of 

 the 6th book. Professor Powell treats the subject in detail, stating 

 the objections which have been urged against Euclid, and presenting 

 answers to these objections. He begins with a general statement of 

 the question; he then proceeds to the consideration of Euclid's 

 method, or the doctrine of comraensurables and incommensurables. 

 He shews that Euclid, in his earlier books, does not even imply the 

 idea of incommensurability. Neither is this introduced in the 5th 

 and 6th books, and it is not till we arrive at the 10th that this 

 edition in geometrical magnitudes, expressed by numerical measures, 

 is broached. In the 11th and 12th books all reference to this dis- 

 tinction is dropped, recurrence being made to the principles of the 

 5th book. It is again, however, resumed in the 13th book, and is 

 applied to various properties. The author observes, *' that much 

 of the confusion of ideas which has arisen on these subjects, has been 

 occasioned by not observing that when we say' two lines are incom^ 

 mensurable, the phrase is, in fact, elliptical, and we ought always 

 to consider as understood, if not expressed, that two lines if referred 

 to numbers are incommensurable. The deficiency of exact comparison 

 in such cases is not in the geometrical relation of the quantities, 



f2 



