Spinoza's Ethics: II.P8: Ideas That Do Not Exist

This proposition addresses the intuition that there must be ideas of singular things which actually don't exist. If II.P7 is correct and the order and connection of ideas is the same as the order and connection of things, then what is the meaning of ideas that do not exist? Here Spinoza says that ideas of singular things which do not exist are in God's infinite idea as formal essences. 

Ideæ rerum singularium sive modorum non existentium ita debent comprehendi in Dei infinita idea ac rerum singularium sive modorum essentiæ formales in Dei attributis continentur.

Translated as,

The ideas of singular things or modes that do not exist ought to be comprehended in the infinite idea of God as the formal essences of singular things or modes are contained in the attributes of God.

Demonstratio: Hæc propositio patet ex præcedenti sed intelligitur clarius ex præcedenti scholio.

Translated as,

This proposition is clear from the preceding [proposition] but is more clearly understood from the preceding scholium.

Corollarium: Hinc sequitur quod quamdiu res singulares non existunt nisi quatenus in Dei attributis comprehenduntur, earum esse objectivum sive ideæ non existunt nisi quatenus infinita Dei idea existit et ubi res singulares dicuntur existere non tantum quatenus in Dei attributis comprehenduntur sed quatenus etiam durare dicuntur, earum ideæ etiam existentiam per quam durare dicuntur, involvent.

Translated as,

From this it follows because as long as singular things do not exist unless insofar as they are comprehended in the attributes of God, the objective essence or ideas of [these singular things] do not exist unless insofar as the infinite idea of God exists and when singular things are said to exist not only insofar as they are comprehended in the attributes of God but insofar are they are said to last, the ideas of [these singular things] involve even existence through which they are said to last.

Scholium: Si quis ad uberiorem hujus rei explicationem exemplum desideret, nullum sane dare potero quod rem de qua hic loquor, utpote unicam adæquate explicet; conabor tamen rem ut fieri potest, illustrare. Nempe circulus talis est naturæ ut omnium linearum rectarum in eodem sese invicem secantium rectangula sub segmentis sint inter se æqualia; quare in circulo infinita inter se æqualia rectangula continentur : attamen nullum eorum potest dici existere nisi quatenus circulus existit nec etiam alicujus horum rectangulorum idea potest dici existere nisi quatenus in circuli idea comprehenditur. Concipiantur jam ex infinitis illis duo tantum nempe E et D existere. Sane eorum etiam ideæ jam non tantum existunt quatenus solummodo in circuli idea comprehenduntur sed etiam quatenus illorum rectangulorum existentiam involvunt, quo fit ut a reliquis reliquorum rectangulorum ideis distinguantur. 

Translated as,

If anyone might desire an example for a more fruitful explanation of this matter, I will be able to give no clear one on the matter about which I speak here, in as much as [the matter] shows up adequately unique. Nevertheless I will try to illustrate the matter so that it might become [clear]. Of course such a circle is of nature so that of all of the straight lines are in the same circle itself in turns cutting up rectangles that are under segments equal among themselves. Thus, in a circle there are infinite equal rectangles contained within itself. Nevertheless not one of them is able to be said to exist unless insofar as it is comprehended in the idea of the circle. Already they are conceived from those infinite [segments] only two - namely E and D - exist. Clearly the ideas of them also do not only exist insofar as they are comprehended in the idea of the circle, but also insofar as they involve the existence of those rectangles, by which it happens that they might be distinguished from the remaining ideas of the remaining rectangles.